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An Atlas of Vertex Degree Polynomials of Graphs of Order at Most Six

Hanan Ahmed, Anwar Alwardi, Ruby Salestina M.

Abstract


Abstract

The vertex degree polynomial of a graph G of order n is defined as V D(G, x) =  åuv∈E(G) d(u)xd(v) where d(u) is the degree of the vertex u [5]. We call the roots of a vertex degree polynomial of a graph the vertex degree roots of that graph. In this article, we compute the vertex degree polynomial of all graphs of order less than or equal six and their roots and present them in tables.

 

Keywords: Adjacent vertex, Vertex degree polynomial, Vertex degree root. Mathematics Subject Classification:


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