Jan 11, 2016 the wiener index wg is popular in chemical literatures. View of total distance, wiener index and opportunity index in. Secondly, we present some sufficient conditions for a nearly balanced bipartite graph. A tribute to claude shannon 19162001 and a plea for. The wiener index of simply generated random trees, random.
We suggest that at the very least, authors should define. The reciprocal complementary wiener rcw index of is defined as, where d is the. Biased richness and evenness relationships within shannon. Scott wiener is a consistent and strong leader on hiv policies, said dr. Wiener index wg of a graph g is the sum of distances between all pairs of vertices in g, i. Maximum wiener index of trees with given segment sequence. Some conclusions on edgevertex szeged index and vertexedge szeged index can refer to 7. The sum of the steiner distances over all sets s of cardinality k is called the steiner k wiener index and studied as the natural generalization of the famous wiener index in chemical graph theory. When index server finds a link to a pdf document on the home page, can it, will it index its content too. Exact formula for computing the hyperwiener index on rows of.
Some calculation results on the wiener complexity and the wiener index of fullerene graphs of order n. Then we characterize the unique hypertrees on n vertices with first three smallest wiener indices, and the unique hypertree not 2uniform with maximum wiener. We suggest an explanation for this dual use of terms and in so doing we offer a tribute to the late claude shannon who passed away on 24 february 2001. Pdfbox is a java api from ben litchfield that will let you access the contents of a pdf document. Wiener index of oddvertexdegree todd trees has been investigated. In the following, we will show di erent formulas for computing the wiener index, in the rst part direct. Bulletin of the australian mathematical society, vol. Natural resource biometrics measures of diversity shannon. It comes with integration classes for lucene to translate a pdf into a lucene document. In this paper we have obtained bounds for the index in terms of eccentricities and given an algorithm to compute the index.
The chemistry and mathematics literature has many results and applications on the wiener index. Extension of the wiener index and wiener polynomial core. A segment of a tree is a path whose ends are branching vertices vertices of degree greater than 2 or leaves, while all other vertices have degree 2. Based on its success, many other topological indexes of chemical graphs, based on information in the distance matrix of the graph, have been developed subsequently to wieners work. Apr 11, 2003 on some occasions it is called the shannonwiener index and on other occasions it is called the shannonweaver index. The fourth section contains a comparative study between the wiener index and several commonly used topological indices in the structureboiling point relationship. Apr 08, 2018 in this paper, we discuss the hamiltonicity of graphs in terms of wiener index, hyper wiener index and harary index of their quasicomplement or complement. The paper outlines the results known for w of trees. A diversity index also called phylogenetic indices or phylogenetic metrics is a quantitative measure that reflects how many different types such as species there are in a dataset a community and that can simultaneously take into account the phylogenetic relations among the individuals distributed among those types, such as richness, divergence or evenness. It appears that for majority of chemical applications, the study of wiener index is restricted to acyclic molecular graphs although mathematical studies are reported for hexagonal systems also see dgkv02.
Price, 1975, where it is known as shannons diversity index, the shannon wiener index, the shannon weaver index and the shannon entropy. X x where du, x is the distance between the vertices u and x in g. The wiener index of a graph g is defined to be 2,, u v g d u. If the files to be indexed include scanned documents, make sure that the text is searchable. The wiener index of a graph g, denoted by wg is the sum of the. Exact formula for computing the hyperwiener index on rows of unit. Using index server 20018 and wanting to index a website and its contents which are in pdf format. We provide formulae for the minimum wiener index of simple triangulations and quadrangulations with given connectedness, and provide the extremal structures which attain these values. The wiener polynomial hg,x has the property that its first derivative evaluated at x1 equals the wiener index, i.
Click add next to include directory to select a folder whose pdf files should be included in the index. The uncertainty is measured by the shannon function h this. Shannonwiener index in a dictionary of environment and conservation. A tribute to claude shannon 19162001 and a plea for more. The selected new developments are briefly described in the fifth section. Singly and doubly vertex weighted wiener polynomials are generalizations of both vertex weighted.
For our uses, this order could be characterized by the number of species andor the number of individuals in each species, within our sample plot. It is the oldest topological index related to molecular branching. The hyperwiener index ww of a graph g is defined as wwg. In this paper, we determine the unique tree that minimises the wiener index, i. In this paper, we first determine the minimum hyperwiener index of graph with connectivity or edgeconnectivity, then present the edgevertex. Since calculating the wiener index of a graph can be computationally expensive, we give some cheaply computable lower and upper bounds for the wiener index given certain graph properties in chapter 3. The wiener index is a graphical invariant that has found extensive application in chemistry. We define a generating function, which we call the wiener polynomial, whose derivative is a qanalog of the wiener index. In this paper, we obtain an explicit expression for the wiener index of an odd graph. On wiener polarity index of bicyclic networks scientific.
The wiener index wg is popular in chemical literatures. The \sl wiener index of a connected graph is the sum of the distances between all unordered pairs of vertices. A child prodigy, wiener later became an early researcher in stochastic and mathematical noise processes, contributing work relevant to electronic engineering, electronic communication, and control systems. The wiener index is named after harry wiener, who introduced it in 1947. Some of those formulas can also be applied to connected graphs. The explicit formulae for the modified wiener index of path, cycle, complete bipartite, cube and lattice graphs are derived and compared with their standard wiener index. As luciano floridi 2010, 2011 stresses, it is a polysemantic concept associated with different phenomena, such as communication, knowledge, reference, meaning, truth, etc. The sum of the steiner distances over all sets s of cardinality k is called the steiner kwiener index and studied as the natural generalization of the famous wiener index in chemical graph theory. Wiener index extension by counting evenodd graph distances. The steiner distance in a graph, introduced by chartrand et al. The lengths of all the segments of a tree form its segment sequence. The wiener filter problem has solutions for three possible cases. Statistics shannon wiener diversity index tutorialspoint. Presentation mode open print download current view.
Wiener index and traceable graphs volume 88 issue 3 lihui yang. Topological graph indices are introduced as mathematical tools for molecule descriptions. Let g v,e be a simple connected graph with vertex set v and edge set e. On some occasions it is called the shannonwiener index and on other occasions it is called the shannonweaver index. In order to index pdf documents you need to first parse them to extract text that you want to index from them. In chemical graph theory, the wiener index also wiener number introduced by harry wiener, is a topological index of a molecule, defined as the sum of the lengths of the shortest paths between all pairs of vertices in the chemical graph representing the nonhydrogen atoms in the molecule. Application of shannons index to study diversity with. Pdf the wiener index of odd graphs semantic scholar. The wiener index of is the sum of all distances between vertices of g. In this paper we study the extremal structures, among trees with a given segment. Shannonwiener index of diversity in a dictionary of plant sciences 2 ed. Firstly, we give some sufficient conditions for an balanced bipartite graph with given the minimum degree to be traceable and hamiltonian, respectively. Norbert wiener november 26, 1894 march 18, 1964 was an american mathematician and philosopher.
All content in this area was uploaded by ash ganagi on sep 20, 2016. The wiener index of simply generated random trees the wiener index of simply generated random trees janson, svante 20030701 00. The structure of graphs with the maximal wiener complexity or the maximal wiener index is discussed, and formulas for the wiener index of several families of graphs are obtained. Exact formula computing the wiener index on rows of unit. Wiener defined wiener index w g 3 and 8 as the sum of smallest distance between all vertices of the graph g w g, i j i j d v v the wiener index w g of a graph g is defined as the sum of the half of the distances between every pair of vertices of g. The wiener index w is the sum of distances between all pairs of vertices of a connected graph. Wiener index of trees as the path and therefore the distance between two vertices of a tree is unique, the wiener index of a tree is much easier to compute than that of an arbitrary graph. Diversity indices that combine both richness and abundance i. First mathematical definition of wiener index, based on the concept of graph theoretical distance as encoded in the distance matrix 11 is due to hosoya 5 since its initiation the wiener index was used in a numerous structureproperty studies 15. I do not seem to be able to get that going pdf exists in central. This equation is probably known, but the author of this text could not find any source. The wiener index of a graph g is the sum of all distances between distinct vertices of the graph g.
Kompanija je osnovana kao green field investicija vienna insurance group wiener stadtische versicherung ag. We consider three different methods for calculating the hyperwiener index of molecular graphs. He was a professor of mathematics at the massachusetts institute of technology mit. This diversity measure is based on information theory. Dpsi log pi, where s is the total number of species in the sample, i is the total number of individuals in. Reciprocal complementary wiener index of a graph g is defined i j as rcw g. Three methods for calculation of the hyperwiener index of. The well known physicochemist harold wiener 4, after whom the index was named, introduced this concept regarding the molecular distance and observed the existence of correlation between this index and numerous physicochemical properties of alkanes. An example of the shannonwiener diversity index for science students. The wiener index, the sum of distances between all pairs of vertices in a connected graph, is a graph invariant much studied in both mathematical and chemical literature. We study some of the elementary properties of this polynomial and compute it. Journal of chemical information and computer sciences 1995, 35 3, 547550. Abstractthe wiener index wg of a connected graph g is defined as the sum of distances between all pairs of vertices.
Beograd na srpskom trzistu posluje od februara 2003. In this paper, we discuss the hamiltonicity of graphs in terms of wiener index, hyperwiener index and harary index of their quasicomplement or complement. Wiener index, number of subtrees, and tree eccentric sequence. A measure used by ecologists when a system contains too many individuals for each to be identified and examined. Statistics shannon wiener diversity index in the literature, the terms species richness and species diversity are sometimes used interchangeably. A centennial symposium was held at the massachusetts institute of technology. The terminal wiener index of a graph is defined as the sum of the distances between the pendent vertices of a graph.
Norbert wiener david jerison and daniel stroock t hrough the week of october 814,1994, a conference entitled the legacy of norbert wiener. The steiner wiener index of trees with a given segment. Thirtytwo richnessbased thirdorder polynomial regression models r 0. A modification of the weiner index which properly takes into account the symmetry of a graph is proposed. If the inline pdf is not rendering correctly, you can download the pdf. In chemical graph theory, the wiener index also wiener number introduced by harry wiener, is a topological index of a molecule, defined as the sum of the lengths of the shortest paths between all pairs of vertices in the chemical graph representing the non hydrogen atoms in the molecule. Shannonwiener index the shannonweaver diversity index is based on communication theory. In this note we consider the problem of maximizing the wiener index among trees with given segment sequence or number of segments, answering two questions proposed in a recent. Here are some pdf parsers that can help you with that. The shannon index has been a popular diversity index in the ecological literature tandon et al.
The wiener index wg of a connected graph g, introduced by wiener in 1947, is defined as wg. We study some of the elementary properties of this polynomial and compute it for some common graphs. The purpose of this analysis was to empirically model and graphically illustrate the numerical relationships between richness s, 435 species and evenness e with respect to shannonwiener index h. If the inline pdf is not rendering correctly, you can download the pdf file here. Al hagri department of computer sciences faculty of sciences university of mohammed v, rabatmorocco email. We obtain results for the terminal wiener index of line graphs. Shannonwiener index of diversity in a dictionary of zoology 3 ed. Wiener index and traceable graphs lihui yang received 16 september 2012. Then enter the name part of your kindle email address below.
For more results on wiener index, we refer to the survey paper 18 written by dobrynin, entringer and gutman and some recent papers 19,20. Wiener, who has been a champion for hiv prevention funding for years, recently helped launch san franciscos getting to zero effort, which aims to end all new hiv infections in san francisco. The steiner distance of vertices in a set s is the minimum size of a connected subgraph that contain these vertices. In the second half of the 20 th century, philosophy begins to direct its attention to this. On reciprocal complementary wiener index of a graph. For more results on wiener index, we refer to the survey paper 18 written by dobrynin, entringer and. Vg du, v where d g u, v is the distance between vertices u and v of g.
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