Journal of Mathematical Chemistry

, Volume 42, Issue 4, pp 775–788

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

Article

## Abstract

The spread s(G) of a graph G is defined as s(G) = maxi,j i  − λ 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 *(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).

## Keywords

spread unicyclic graph characteristic polynomial eigenvalue

## AMS subject classification

05C50 15A42 15A36

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