TY - JOUR
ID - 854
TI - MORE ON EDGE HYPER WIENER INDEX OF GRAPHS
JO - Journal of Algebraic Systems
JA - JAS
LA - en
SN - 2345-5128
AU - Alhevaz, A.
AU - Baghipur, M.
AD - Department of Mathematics, Shahrood University of Technology, P.O. Box: 316-
3619995161, Shahrood, Iran.
Y1 - 2017
PY - 2017
VL - 4
IS - 2
SP - 135
EP - 153
KW - Edge-hyper Wiener index
KW - line graph
KW - Gutman index
KW - connectivity
KW - edge-transitive graph
DO - 10.22044/jas.2017.854
N2 - Let G=(V(G),E(G)) be a simple connected graph with vertex set V(G) and edge set E(G). The (first) edge-hyper Wiener index of the graph G is defined as: $$WW_{e}(G)=\sum_{\{f,g\}\subseteq E(G)}(d_{e}(f,g|G)+d_{e}^{2}(f,g|G))=\frac{1}{2}\sum_{f\in E(G)}(d_{e}(f|G)+d^{2}_{e}(f|G)),$$ where de(f,g|G) denotes the distance between the edges f=xy and g=uv in E(G) and de(f|G)=∑g€(G)de(f,g|G). In this paper we use a method, which applies group theory to graph theory, to improving mathematically computation of the (first) edge-hyper Wiener index in certain graphs. We give also upper and lower bounds for the (first) edge-hyper Wiener index of a graph in terms of its size and Gutman index. Also we investigate products of two or more graphs and compute the second edge-hyper Wiener index of the some classes of graphs. Our aim in last section is to find a relation between the third edge-hyper Wiener index of a general graph and the hyper Wiener index of its line graph. of two or more graphs and compute edge-hyper Wiener number of some classes of graphs.
UR - https://jas.shahroodut.ac.ir/article_854.html
L1 - https://jas.shahroodut.ac.ir/article_854_2486403d0b8da2a0bb248f7cd1fcd96b.pdf
ER -