Graph polynomials serve as robust algebraic encodings of the intricate combinatorial properties inherent to graphs. At the heart of this discipline lies the Tutte polynomial, an invariant that not ...
Abstract. Let 𝐼(𝐺;𝑥) denote the independence polynomial of a graph 𝐺. In this paper we study the unimodality properties of 𝐼(𝐺;𝑥) for some composite graphs 𝐺. Given two graphs 𝐺₁ and 𝐺₂, let ...
Inspired by Rearick's work on logarithm and exponential functions of arithmetic functions, we introduce two new operators, LOG and EXP. The LOG operates on generalized Fibonacci polynomials giving ...
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