University of KashanIranian Journal of Mathematical Chemistry2228-648911220200701On Edge Mostar Index of Graphs9510611078010.22052/ijmc.2020.221320.1489ENHechaoLiuCollege of Mathematics and Statistics
Hunan Normal UniversityLingSongCollege of Mathematics and Statistics
Hunan Normal UniversityQiqiXiaoCollege of Mathematics and Statistics
Hunan Normal UniversityZikaiTangSchool of Mathematics and Statistics, Hunan Normal University0000-0002-2577-7890Journal Article20200225The edge Mostar index 𝑀𝑜𝑒(𝐺) of a connected graph 𝐺 is defined as 𝑀𝑜𝑒(𝐺)=Σ𝑒=𝑢𝑣∈𝐸(𝐺) |𝑚𝑢(𝑒|𝐺)−𝑚𝑣(𝑒|𝐺)|, where 𝑚𝑢(𝑒|𝐺)and 𝑚𝑣(𝑒|𝐺) are, respectively, the number of edges of 𝐺 lying closer to vertex 𝑢 than to vertex 𝑣 and the number of edges of 𝐺 lying closer to vertex 𝑣 than to vertex 𝑢. In this paper, we determine the extremal values of edge Mostar index of some graphs. We characterize extremal trees, unicyclic graphs and determine the extremal graphs with maximum and second maximum edge Mostar index among cacti with size 𝑚 and 𝑡 cycles. At last, we give some open problems.https://ijmc.kashanu.ac.ir/article_110780_6c7ca696f01b7ecfc6543d510880bef9.pdf