Maximum values of the edge Mostar index in tricyclic graphs

Abstract

For a graph G, the edge Mostar index of G is the sum of |mu (e|G)-mv (e|G)| over all edges e = uv of G, where mu (e|G) denotes the number of edges of G that have a smaller distance in G to u than to v, and analogously for mv (e|G). This paper mainly studies the problem of determining the graphs that maximize the edge Mostar index among tricyclic graphs. To be specific, we determine a sharp upper bound for the edge Mostar index on tricyclic graphs and identify the graphs that attain the bound.