Title of article :
On Edge Mostar Index of Graphs
Author/Authors :
LIU, HECHAO School of Mathematics and Statistics - Hunan Normal University - Changsha - Hunan 410081 - P. R. China - School of Mathematical Sciences - South China Normal University - Guangzhou - 510631, P. R. China , SONG, LING School of Mathematics and Statistics - Hunan Normal University - Changsha - Hunan 410081 - P. R. China , XIAO, QIQI School of Mathematics and Statistics - Hunan Normal University - Changsha - Hunan 410081 - P. R. China , TANG, ZIKAI School of Mathematics and Statistics - Hunan Normal University - Changsha - Hunan 410081 - P. R. China
Abstract :
The edge Mostar index )ܩ(ܯof a connected graph ܩis defined ܯas
(∑ = )ܩୀ௨௩(ீ) | ݉௨(݁|݉ − )ܩ௩(݁| ,|)ܩwhere ݉௨(݁|)ܩand ݉ ௩(݁| )ܩare, respectively, the number of edges of ܩlying closer to vertex ݑthan to vertex ݒand the number of edges of ܩlying closer
to vertex ݒthan to vertex .ݑIn 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 ݉ and ݐcycles. At last, we give some open problems.
Keywords :
Edge Mostar index , Tree , Unicyclic graph , Cacti , Extremal value
Journal title :
Iranian Journal of Mathematical Chemistry
