Distribution of zeros of matching polynomials of hypergraphs

. Let H be a connected k -graph with maximum degree ∆ ≥ 2 and let µ ( H , x ) be the matching polynomial of H . In this paper, we devote to studying the distribution of zeros of the matching polynomials of k -graphs. We prove that the zeros (with multiplicities) of µ ( H , x ) are invariant under a rotation of an angle 2 π/ℓ in the complex plane for some positive integer ℓ and k is the maximum integer with this property. Let λ ( H ) denote the maximum modulus of all zeros of µ ( H , x ). We show that λ ( H ) is a simple root of µ ( H , x ) and To achieve these, we introduce the path tree T ( H , u ) of H with respect to a vertex u of H , which is a k -tree, and prove that which generalizes the Godsil’s identity ( Matchings and walks in graphs. J. Graph Theory 5 (1981) 285–297) on the matching polynomial of graphs.

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