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Title: Relations and bounds for the zeros of graph polynomials using vertex orbits
In this paper, we prove bounds for the unique, positive zero of O  G (z) := 1 −O G (z) , where O G ( z ) is the so-called orbit polynomial [1]. The orbit polynomial is based on the multiplic- ity and cardinalities of the vertex orbits of a graph. In [1] , we have shown that the unique, positive zero δ≤1 of O  G (z) can serve as a meaningful measure of graph symmetry. In this paper, we study special graph classes with a specified number of orbits and obtain bounds on the value of δ.
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Applied mathematics and computation
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National Science Foundation
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