Title of article :
On the Revised Edge-Szeged Index of Graphs
Author/Authors :
LIU, HECHAO Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education) - College of Mathematics and Statistics - Hunan Normal University, Changsha, P. R. China , YOU, LIHUA School of Mathematical Sciences - South China Normal University, Guangzhou, 510631, P. R. China , TANG, ZIKAI Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education) - College of Mathematics and Statistics - Hunan Normal University, Changsha, P. R. China
Abstract :
The revised edge-Szeged index of a connected graph G is defined as
Sze∗(G) = Σ e=uve∈E(G) (mu(e∣G)+ mo(e∣G/2)(mv(e∣G)✚m0(e∣G)/2)
, where mu(e∣G), mv(e|G) and m0(e|G) are, respectively, the number of edges of G lying closer to vertex u than to vertex v, the number of edges of G lying closer to vertex v than to vertex u, and the number of edges equidistant to u and v. In this paper, we give an effective method for computing the revised edge-Szeged index of unicyclic graphs and using this result we identify the minimum revised edge-Szeged index of conjugated unicyclic graphs which is defined as the unicyclic graphs with a perfect matching. We also give a method of
calculating revised edge-Szeged index of the joint graph.
Keywords :
Join graph , Conjugated unicyclic graph , Revised edge-Szeged index
