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# The spread of unicyclic graphs with given size of maximum matchings

Nankai University, T’ien-ching-shih, Tianjin Shi, China
(Impact Factor: 1.27). 11/2007; 42(4):775-788. DOI: 10.1007/s10910-006-9141-6

ABSTRACT The spread s(G) of a graph G is defined as s(G)=max The spread s(G) of a graph G is defined as s(G)=max
i,j i,j
|λ |λ
i i
−λ −λ
j j
|, where the maximum is taken over all pairs of eigenvalues of G. Let U(n,k) denote the set of all unicyclic graphs on n vertices with a maximum matching of cardinality k, and U |, where the maximum is taken over all pairs of eigenvalues of G. Let U(n,k) denote the set of all unicyclic graphs on n vertices with a maximum matching of cardinality k, and U
*(n,k) the set of triangle-free graphs in U(n,k). In this paper, we determine the graphs with the largest and second largest spectral radius in U *(n,k) the set of triangle-free graphs in U(n,k). In this paper, we determine the graphs with the largest and second largest spectral radius in U
*(n,k), and the graph with the largest spread in U(n,k). *(n,k), and the graph with the largest spread in U(n,k).

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