Maximal Unicyclic Graphs With Respect to New Atom-bond Connectivity Index.

The concept of atom-bond connectivity (ABC) index was introduced in the chemical graph theory in 1998. The atom-bond connectivity (ABC) index of a graph G defined as ABC(G) = ... √di + dj - 2/didj where E(G) is the edge set and d is the degree of vertex vi of G. Very recently Graovac et al. define a new version of the ABC index as ABC2 = ... √ni + j - 2/ninj where ni denotes the number of vertices of G whose distances to vertex vi are smaller than those to the other vertex vj of the edge e = vivj, and nj is defined analogously. In this paper we determine the maximal unicyclic graphs with respect to new atom-bond connectivity index (ABC2). [ABSTRACT FROM AUTHOR]