Some new inequalities concerning the variable sum exdeg index/coindex of graphs

Author:

Ali Akbar1,Milovanovic Emina2,Matejic Marjan2ORCID,Milovanovic Igor2ORCID

Affiliation:

1. Department of Mathematics, Faculty of Science, University of Háil, Háil, Saudi Arabia

2. Faculty of Electronic Engineering, University of Niš, Niš, Serbia

Abstract

The variable sum exdeg index and coindex of a graph G are denoted by SEIa(G) and ?SEIa(G), respectively, and they are defined as SEIa(G) = ?n,i=1 diadi and SEIa(G) = ?n,i =1(n?1?di)adi, respectively, where ?a? is a positive real number different from 1 and (d1, d2,..., dn) is the vertex-degree sequence of G. The present paper gives several new inequalities involving the graph invariants SEIa and/or ?SEIa. All graphs attaining the equality signs in the obtained inequalities are also characterized.

Publisher

National Library of Serbia

Reference22 articles.

1. A. Ali, D. Dimitrov, On the extremal graphs with respect to bound incident degree indices, Discr. Appl. Math. 238 (2018) 32-40.

2. A. Ali, E. Milovanović, M. Matejić, I. Milovanović, On the variable sum exdeg index/coindex of graphs, MATCH Commun. Math. Comput. Chem., in press.

3. J. A. Bondy, U. S. R. Murty, Graph Theory, Springer, London, 2008.

4. W. Carballosa, J. M. Rodríguez, J. M. Sigarreta, Extremal problems on the variable sum exdeg index, MATCH Commun. Math. Comput. Chem. 84 (2020) 753-772.

5. G. Chartrand, L. Lesniak, P. Zhang, Graphs & Digraphs, Sixth Edition, CRC Press, Boca Raton, 2016.

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