on the revised edgeszeged index of graphs

The revised edgeszeged index of a connected graph $g$ is defined as sze*(g)=∑e=uv∊e(g)( (mu(e|g)+(m0(e|g)/2)(mv(e|g)+(m0(e|g)/2) ), where mu(e|g), mv(e|g) and m0(e|g) are, respectively, the number of edges of g lying closer to vertex u than to vertex v, the number of edges of g lying closer to vertex v than to vertex u, and the number of edges equidistant to u and v. in this paper, we give an effective method for computing the revised edgeszeged index of unicyclic graphs and using this result we identify the minimum revised edgeszeged index of conjugated unicyclic graphs (i.e., unicyclic graphs with a perfect matching). we also give a method of calculating revised edgeszeged index of the joint graph.