The spread of unicyclic graphs with given size of maximum matchings

ArticleinJournal of Mathematical Chemistry 42(4):775-788 · November 2007with6 Reads
Impact Factor: 1.15 · 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).