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.