The vertex PI index of a graph G is the sum over all edges uv β E(G) of the number of vertices which are not equidistant to u and v. In this paper, the extremal values of this new topological index are computed. In particular, we prove that for each n-vertex graph 2 , where x denotes the greatest i
The PI index of product graphs
β Scribed by H. Yousefi-Azari; B. Manoochehrian; A.R. Ashrafi
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 178 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0893-9659
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β¦ Synopsis
The Padmakar-Ivan index of a graph G is the sum over all edges uv of G of number of edges which are not equidistant from u and v. In this work, an exact expression for the PI index of the Cartesian product of bipartite graphs is computed. Using this formula, the PI indices of C 4 nanotubes and nanotori are computed.
π SIMILAR VOLUMES
The PI index is a graph invariant defined as the summation of the sums of n eu (e|G) and n ev (e|G) over all the edges e = uv of a connected graph G, i.e., PI(G) = eβE(G) [n eu (e|G) + n ev (e|G)], where n eu (e|G) is the number of edges of G lying closer to u than to v and n ev (e|G) is the number
## Abstract The __circular chromatic index__ of a graph __G__, written $\chi\_{c}'(G)$, is the minimum __r__ permitting a function $f : E(G)\rightarrow [0,r)$ such that $1 \le | f(e)-f(e')|\le r - 1$ whenever __e__ and $e'$ are incident. Let $G = H$ β‘ $C\_{2m +1}$, where β‘ denotes Cartesian product
## Abstract This article proves the following result: Let __G__ and __G__β² be graphs of orders __n__ and __n__β², respectively. Let __G__^\*^ be obtained from __G__ by adding to each vertex a set of __n__β² degree 1 neighbors. If __G__^\*^ has game coloring number __m__ and __G__β² has acyclic chromat