Spectral Sufficient Conditions for Graph Factors

2025/02/01 by Ren, Fengyun, Zhang, Shumin, Wang, Ke
#Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.00405

Abstract

The \K_1,1, K_1,2,C_m: m≥3\-factor of a graph is a spanning subgraph whose each component is an element of \K_1,1, K_1,2,C_m: m≥3\. In this paper, through the graph spectral methods, we establish the lower bound of the signless Laplacian spectral radius and the upper bound of the distance spectral radius to determine whether a graph admits a \K₂\-factor. We get a lower bound on the size (resp. the spectral radius) of G to guarantee that G contains a \K_1,1, K_1,2,C_m: m≥3\-factor. Then we determine an upper bound on the distance spectral radius of G to ensure that G has a \K_1,1, K_1,2,C_m: m≥3\-factor. Furthermore, by constructing extremal graphs, we show that the above all bounds are best possible.

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