The Laplacian matching polynomial of a graph G, denoted by LM(G,x), is a new graph polynomial whose all zeros are nonnegative real numbers. In this paper, we investigate the location of zeros of the Laplacian matching polynomials. Let G be a connected graph. We show that 0 is a zero of LM(G,x) if and only if G is a tree. We prove that the number of distinct positive zeros of LM(G,x) is at least equal to the length of the longest path in G. It is also established that the zeros of LM(G,x) and LM(G-e,x) interlace for each edge e of G. Using the path tree of G, we present a linear algebraic approach to investigate the largest zero of LM(G,x) and particularly to give tight upper and lower bounds on it.
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