On The Minimal ABC Index of Connected Graphs with Given Degree Sequence
نویسندگان
چکیده
The atom-bond connectivity (ABC) index of a graph ( , ) G V E is defined as ( ) [ ( ) ( ) 2] / [ ( ) ( )] i j i j i j v v E ABC G d v d v d v d v , where ( ) i d v denotes the degree of the vertex i v of G . This recently introduced molecular structure descriptor found interesting applications in the study of the heats of formation of alkanes. Let ( ) C and ( ) T denote the sets of connected graphs and trees with degree sequence , respectively. Gan et al. [MATCH Commun. Math. Comput. Chem. 68 (2012)] and Xing et al. [Filomat 26 (2012)] proved that, the so-called greedy tree is a tree with minimal ABC index in ( ) T . In this paper we introduce the breadth-first searching graphs (BFS-graphs for short), and prove that, for any degree sequence there exists a BFS-graph with minimal ABC index in ( ) C . This result is applicable to obtain the minimal value or lower bounds of ABC index of connected graphs.
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