Maxima of the A α -Index of Non-Bipartite C 3 -Free Graphs for 1/2 < α < 1

Haixia Zhang () and Yu Lei
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Haixia Zhang: Department of Mathematics, Taiyuan University of Science and Technology, Taiyuan 030024, China
Yu Lei: Department of Mathematics, Taiyuan University of Science and Technology, Taiyuan 030024, China

Mathematics, 2025, vol. 13, issue 3, 1-18

Abstract: In 2017, Nikiforov defined the A α -matrix of the graph G as A α ( G ) = α D ( G ) + ( 1 − α ) A ( G ) , 0 ≤ α ≤ 1 , which merges the diagonal degree matrix D ( G ) and the adjacency matrix A ( G ) . In this paper, we characterize the graphs which attain the maximum A α -index among triangle-free non-bipartite graphs of order n for 1 / 2 < α < 1 .

Keywords: A ? -matrix; A ? -index; non-bipartite graph; triangle-free graph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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