The spectral radius of graphs with no odd wheels

2021/04/15 by Cioabă, Sebastian, Desai, Dheer Noal, Tait, Michael · 7 citations
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2104.07729

Abstract

The odd wheel W_2k+1 is the graph formed by joining a vertex to a cycle of length 2k. In this paper, we investigate the largest value of the spectral radius of the adjacency matrix of an n-vertex graph that does not contain W_2k+1. We determine the structure of the spectral extremal graphs for all k≥ 2, k\not∈ \4,5\. When k=2, we show that these spectral extremal graphs are among the Turán-extremal graphs on n vertices that do not contain W_2k+1 and have the maximum number of edges, but when k≥ 9, we show that the family of spectral extremal graphs and the family of Turán-extremal graphs are disjoint.

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• Spectral Turán problems for suspensions of balanced trees
• Non-bipartite graphs without theta subgraphs
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• The spectral Turán problem: Characterizing spectral-consistent graphs
• Spectral Turán-type problem in non-r-partite graphs: Forbidden generalized book graph B_r,k
• Spectral extrema of graphs forbidding a fan

Related

• More results on the spectral radius of graphs with no odd wheels
• The maximum spectral radius of wheel-free graphs
• Adjacency eigenvalues of graphs without short odd cycles
• On a conjecture of spectral extremal problems
• Spectral extremal problem for the odd prism