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

#### Abstract

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 (see formula in text) where E(G) is the edge set and di is the degree of vertex v(i) of G. Very recently Graovac et al. define a new version of the ABC index as (see formula in text) where n(i) denotes the number of vertices of G whose distances to vertex v(i) are smaller than those to the other vertex v(j) of the edge e = v(i) v(j), and n(j) is defined analogously. In this paper we determine the maximal unicyclic graphs with respect to new atom-bond connectivity index (ABC2).

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#### Keywords

Unicyclic graph, Atom-bond connectivity (ABC) index, New atom-bond connectivity (ABC2) index, Upper bound

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Copyright (c) 2013 Kinkar Ch. Das, Kexiang Xu, Ante Graovac

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