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- W4362631084 abstract "In this paper we consider the extremal problem on adjacency spectral radius of {C3,C5}-free graphs. Assume that G is a graph with m edges having no isolated vertices, and let λ be the spectral radius of its adjacency matrix. Firstly, by using the method of characterizing {C3,C5}-free non-bipartite graphs whose second largest eigenvalue is less than 54, we show that, if G is a {C3,C5}-free non-bipartite graph of size m, thenλ⩽∑u∈VGd(u)2−m+4f−54. Equality holds if and only if G≅C7, where d(u) is the degree of vertex u and f denotes the number of 4-cycles in G. Secondly, we show that, if G is a {C3,C5}-free non-bipartite graph of odd size m, then λ⩽θ(m) with equality if and only if G≅RK2,m−32, where θ(m) is the largest root ofx4−x3−(m−3)x2+(m−4)x+m−5=0 and RK2,m−32 is obtained by replacing an edge of the complete bipartite graph K2,m−32 with P5." @default.
- W4362631084 created "2023-04-07" @default.
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- W4362631084 date "2023-07-01" @default.
- W4362631084 modified "2023-09-29" @default.
- W4362631084 title "The maximum spectral radius of {C3,C5}-free graphs of given size" @default.
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- W4362631084 doi "https://doi.org/10.1016/j.disc.2023.113440" @default.
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