Extremal Structure on Revised Edge-Szeged Index with Respect to Tricyclic Graphs

For a given graph G, Sze*(G)=∑e=uv∈E(G)mu(e)+m0(e)2mv(e)+m0(e)2 is the revised edge-Szeged index of G, where mu(e) and mv(e) are 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, respectively, and m0(e) is the number of edges equidistant to u and v. In this paper, we identify the lower bound of the revised edge-Szeged index among all tricyclic graphs and also characterize the extremal structure of graphs that attain the bound.