TY - JOUR
ID - 102191
TI - On the Revised Edge-Szeged Index of Graphs
JO - Iranian Journal of Mathematical Chemistry
JA - IJMC
LA - en
SN - 2228-6489
AU - Liu, Hechao
AU - You, Lihua
AU - Tang, Zikai
AD - School of Mathematics and Statistics, Hunan Normal University, Changsha City, Hunan Province, China
AD - School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P.R. China
Y1 - 2019
PY - 2019
VL - 10
IS - 4
SP - 279
EP - 293
KW - Revised edge-Szeged index
KW - Conjugated unicyclic graph
KW - Join graph
DO - 10.22052/ijmc.2019.200349.1460
N2 - 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.
UR - https://ijmc.kashanu.ac.ir/article_102191.html
L1 - https://ijmc.kashanu.ac.ir/article_102191_dd77ab587a307bd7e4971623d96ef182.pdf
ER -