Further results on the largest matching root of unicyclic graphs

Abstract

© 2017 Elsevier B.V. Let G be a simple connected graph with vertex set V(G). The matching polynomial of G is defined as MG(x)=∑k=0n∕2(−1)km(G,k)xn−2k, where m(G,k) denotes the number of ways in which k independent edges can be selected in G. Let λ1(G) be the largest root of MG(x). We determine the unicyclic graphs with the four largest and the two smallest λ1(G)-values.