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

# 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).

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).

- CitationsCitations10
- ReferencesReferences20

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