On the spectral radius of bi-block graphs with given independence number α

Joyentanuj Das and Sumit Mohanty

Applied Mathematics and Computation, 2021, vol. 402, issue C

Abstract: A connected graph is called a bi-block graph if each of its blocks is a complete bipartite graph. Let B(k,α) be the class of bi-block graph on k vertices with given independence number α. It is easy to see that every bi-block graph is a bipartite graph. For a bipartite graph G on k vertices, the independence number α(G) satisfies ⌈k2⌉≤α(G)≤k−1. In this article, we prove that the maximum spectral radius ρ(G) among all graphs G in B(k,α), is uniquely attained for the complete bipartite graph Kα,k−α.

Keywords: Complete bipartite graphs; Bi-block graphs; Independence number; Spectral radius (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:402:y:2021:i:c:s0096300320308651

DOI: 10.1016/j.amc.2020.125912

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