Further results on the largest matching root of unicyclic graphs

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

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