University of KashanIranian Journal of Mathematical Chemistry2228-648910420191201On the Revised Edge-Szeged Index of Graphs27929310219110.22052/ijmc.2019.200349.1460ENHechaoLiuSchool of Mathematics and Statistics, Hunan Normal University, Changsha City, Hunan Province, China0000-0001-7606-4842LihuaYouSchool of Mathematical Sciences, South China Normal University, Guangzhou 510631, P.R. ChinaZikaiTangSchool of Mathematics and Statistics, Hunan Normal University, Changsha City, Hunan Province, China0000-0002-2577-7890Journal Article20190903The revised edge-Szeged index of a connected graph $G$ is defined as Sz<sub>e</sub>*(G)=∑<sub>e=uv∊E(G)</sub>( (m<sub>u</sub>(e|G)+(m<sub>0</sub>(e|G)/2)(m<sub>v</sub>(e|G)+(m<sub>0</sub>(e|G)/2) ), where m<sub>u</sub>(e|G), m<sub>v</sub>(e|G) and m<sub>0</sub>(e|G) are, respectively, the number of edges of <em>G</em> lying closer to vertex <em>u</em> than to vertex <em>v</em>, the number of edges of <em>G</em> lying closer to vertex <em>v</em> than to vertex <em>u</em>, and the number of edges equidistant to <em>u</em> and <em>v</em>. 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.https://ijmc.kashanu.ac.ir/article_102191_dd77ab587a307bd7e4971623d96ef182.pdf