New Lower Bounds for the First Variable Zagreb Index

2018/06/06 by Martínez-Pérez, Alvaro, Rodríguez, José M.
#05C07 #92E10 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.02063

Abstract

The aim of this paper is to obtain new sharp inequalities for a large family of topological indices, including the first variable Zagreb index M₁^α, and to characterize the set of extremal graphs with respect to them. Our main results provide lower bounds on this family of topological indices involving just the minimum and the maximum degree of the graph. These inequalities are new even for the first Zagreb, the inverse and the forgotten indices.

Related

• New improved lower bounds for Zagreb indices of graphs
• Upper and lower bounds for topological indices on unicyclic graphs
• Extremal graphs with maximum complementary second Zagreb index
• On extremal values of some degree-based topological indices with a forbidden or a prescribed subgraph
• On the sharp lower bounds of Zagreb indices of graphs with given number of cut vertices