Abstract

Let G(V,E) be a simple graph of order n with vertex set V and edge set E. Let (u, v) denotes an unordered vertex pair of distinct vertices of G. The i-common neighbor set of G is dened as N(G, i) := {(u; v) : u; v ∈ V; u ≠ v and |N(u) ∩ N(v)| = i}, for 0 ≤ i ≤ n-2. The polynomial N[G; x] = ∑_i=0^(n-2) |N(G; i)|xⁱ is defined as the common neighbor polynomial of G. A root of the polynomial N[G; x] is defined as the common neighbor root of the graph G. In this paper we study the stability of common neighbor polynomial of some graphs.

Keywords and Phrases

Common neighbor polynomial, common neighbor root.

A.M.S. subject classification

05C31, 05C39.

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