%0 Journal Article
%T On the Revised Edge-Szeged Index of Graphs
%J Iranian Journal of Mathematical Chemistry
%I University of Kashan
%Z 2228-6489
%A Liu, Hechao
%A You, Lihua
%A Tang, Zikai
%D 2019
%\ 12/01/2019
%V 10
%N 4
%P 279-293
%! On the Revised Edge-Szeged Index of Graphs
%K Revised edge-Szeged index
%K Conjugated unicyclic graph
%K Join graph
%R 10.22052/ijmc.2019.200349.1460
%X The revised edge-Szeged index of a connected graph $G$ is defined as Sze*(G)=∑e=uv∊E(G)( (mu(e|G)+(m0(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 (i.e., unicyclic graphs with a perfect matching). We also give a method of calculating revised edge-Szeged index of the joint graph.
%U https://ijmc.kashanu.ac.ir/article_102191_dd77ab587a307bd7e4971623d96ef182.pdf