On edge Mostar index of graphs

Document Type: Research Paper

Authors

1 College of Mathematics and Statistics Hunan Normal University

2 School of Mathematics and Statistics, Hunan Normal University

10.22052/ijmc.2020.221320.1489

Abstract

The edge Mostar index π‘€π‘œπ‘’(𝐺) of a connected graph 𝐺 is defined as π‘€π‘œπ‘’(𝐺)=Σ𝑒=𝑒𝑣∈𝐸(𝐺) |π‘šπ‘’(𝑒|𝐺)−π‘šπ‘£(𝑒|𝐺)|, where π‘šπ‘’(𝑒|𝐺)and π‘šπ‘£(𝑒|𝐺) are, respectively, the number of edges of 𝐺 lying closer to vertex 𝑒 than to vertex 𝑣 and the number of edges of 𝐺 lying closer to vertex 𝑣 than to vertex 𝑒. 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 π‘š and 𝑑 cycles. At last, we give some open problems.

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