New lower bounds for the second variable Zagreb index

Álvaro Martínez-Pérez () and José M. Rodríguez ()
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Álvaro Martínez-Pérez: Facultad CC. Sociales de Talavera
José M. Rodríguez: Universidad Carlos III de Madrid

Journal of Combinatorial Optimization, 2018, vol. 36, issue 1, No 16, 194-210

Abstract: Abstract The aim of this paper is to obtain new sharp inequalities for a large family of topological indices, including the second variable Zagreb index $$M_2^{\alpha }$$ M 2 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 Randić, the second Zagreb and the modified Zagreb indices.

Keywords: Second variable Zagreb index; Graph invariant; Vertex-degree-based graph invariant; Topological index; MSC 05C07; MSC 92E10 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10878-018-0293-7

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