Walks, infinite series and spectral radius of graphs
Abstract
For a graph G, the spectral radius ho(G) of G is the largest eigenvalue of its adjacency matrix. In this paper, we seek the relationship between ho(G) and the walks of the subgraphs of G. Especially, if G contains a complete multi-partite graph as a spanning subgraph, we give a formula for ho(G) by using an infinite series on walks of the subgraphs of G. These results are useful for the current popular spectral extremal problem.
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