On some graphic polynomials whose zeros are real

Ivan Gutman

Abstract: Polynomials which are formed by linear combination of the characteristic polynomial of a graph $\,G\,$ and the characteristic polynomials of the vertex-deleted subgraphs of $\,G\,$ have real zeros. The same is true for the linear combination of the matching polynomial of $\,G\,$ and the matching polynomials of the vertex-deleted subgraphs of $\,G\,$. Several statements about the location of the zeros of these polynomials are obtained.

Classification (MSC2000): 05C55

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