Wiener index of path graph
10 Jul 2019 graph. In chemical graph theory the Wiener index of a graph G, denoted by W(G) and Hyper Wiener indices of Unitary addition Cayley graph Gn is computed. of hyper-Wiener index for cycle-containing structures, J. Chem. 13 Jul 2016 The Wiener index is the sum of distances between all pairs of m≥3; i.e., a graph consisting of a cycle Cnm with one additional vertex which is 15 Jan 2015 Hyper-Wiener index of gear fan graph, gear wheel graph and their r-corona vertex in every two adjacent vertices of the fan path Pn of fan. of the graph G and ij d is the distance (i.e., the number of edges of a shortest path ) between the vertices i v and j v . The relation between Wiener index. ( ). The Wiener index for complete graph is. 2. 2. n n. -. , and Wiener index for path graph is. 3. 6 n n. -. , The wiener index for the cycle graph is w(Cn)=. 2−1.
The terminal Wiener index of a graph is defined as the sum of the distances between the pendent vertices of a graph. We obtain results for the terminal Wiener index of line graphs. View
The distance of between any two vertices u and v of graph is defined as the length of the shortest path connecting u, v is d (u, v).A topological index is a number. Wiener Index of a Cycle in the Context of Some Graph Operations. 3. • Graphs with boxicity k ( S is the set of boxes of dimension k ). • Line graphs ( S is the set of Keywords: Degree Distance; Wiener Index; Cacti. 1. The Wiener index of a graph is the sum of the neighbor of x on the shortest path between x and y and. 3 Oct 2015 Among 2-connected graphs on n vertices (or even stronger, among the graphs of minimum degree 2), the n-cycle has the largest Wiener index. 1 Jan 1995 Three Methods for Calculation of the Hyper-Wiener Index of Molecular Graphs. Journal of Chemical Information and Computer Sciences 2002,
Finally in Section 4 we compute the Wiener index of trees which are constructed by replacing each edge by a path of length t . Then as a corollary, we obtain the
The terminal Wiener index of a graph is defined as the sum of the distances between the pendent vertices of a graph. We obtain results for the terminal Wiener index of line graphs. View
where dG.u;v/ is the shortest path distance between vertices u and v in G. Details on the Wiener index can be found in [7, 8, 12, 14, 15]. Edge versions of the
The Wiener index W, denoted w (Wiener 1947) and also known as the "path number" or Wiener number (Plavšić et al. 1993), is a graph index defined for a graph on n nodes by W=1/2sum_(i=1)^nsum_(j=1)^n(d)_(ij), where (d)_(ij) is the graph distance matrix. Unless otherwise stated, hydrogen atoms are usually ignored in the computation of such indices as organic chemists usually do when they write Also as an application we compute the Wiener index of graphs introduced in . Finally in Section 4 we compute the Wiener index of trees which are constructed by replacing each edge by a path of length t. Then as a corollary, we obtain the result given in . Wiener index. The Wiener index of a vertex is the sum of the shortest path distances between v and all other vertices. The Wiener index of a graph G is the sum of the shortest path distances over all pairs of vertices. Used by mathematical chemists (vertices = atoms, edges = bonds). Random walk. networkx.algorithms.wiener.wiener_index¶ wiener_index (G, weight=None) [source] ¶. Returns the Wiener index of the given graph. The Wiener index of a graph is the sum of the shortest-path distances between each pair of reachable nodes. For pairs of nodes in undirected graphs, only one orientation of the pair is counted. The Wiener index W(G) of a connected graph G is the sum of the distances between all pairs (ordered) of vertices of G. ∑, , . In this paper, we give theoretical results for calculating the Wiener index of a cycle in the context of some graph operations. These formulas will pave the way to demonstrate the Wiener index of molecular structures. The Wiener index of a graph is the sum of the distances between all pairs of vertices. It has been one of main descriptors that correlate a chemical compound's molecular graph with experimentally gathered data regarding the compound's characteristics. We characterize graphs with the maximum Wiener index among all graphs of order . with radius The Wiener index of a graph G is defined as W(G)=∑ u,v d G (u,v), where d G (u,v) is the distance between u and v in G, and the sum goes over all pairs of vertices.
22 Jun 2017 Keywords: Distance in graphs, Wiener index, peripheral Wiener index two vertices u and v of G is the length of a shortest path between u and
“The Wiener index of a graph is represented by and defined as the sum of distances between all pairs of vertices in a simple graph ”: Based on the Wiener index, Hosoya introduced the Wiener polynomial (now called Hosoya polynomial) in 1988 [ 8 ]. The Wiener index of a graph is defined as the sum of distances be-tween all pairs of vertices in a connected graph. Wiener index correlates well with many physio chemical properties of organic compounds and as such has been well studied over the last quarter of a century. In this paper we prove some general results on Wiener Index for graphs using We show that among all graphs on n vertices which have p≥2 blocks, the maximum Wiener index is attained by a graph composed of two cycles joined by a path (here we admit that one or both cycles The terminal Wiener index of a graph is defined as the sum of the distances between the pendent vertices of a graph. We obtain results for the terminal Wiener index of line graphs. View The Wiener index W, denoted w (Wiener 1947) and also known as the "path number" or Wiener number (Plavšić et al. 1993), is a graph index defined for a graph on n nodes by W=1/2sum_(i=1)^nsum_(j=1)^n(d)_(ij), where (d)_(ij) is the graph distance matrix. Unless otherwise stated, hydrogen atoms are usually ignored in the computation of such indices as organic chemists usually do when they write Also as an application we compute the Wiener index of graphs introduced in . Finally in Section 4 we compute the Wiener index of trees which are constructed by replacing each edge by a path of length t. Then as a corollary, we obtain the result given in .
The Wiener index of a graph G is defined as W(G)=∑ u,v d G (u,v), where d G (u,v) is the distance between u and v in G, and the sum goes over all pairs of vertices.