Skolem Mean Labeling Of Four Star Graphs K_(1,a_1) ∪K_(1,a_2) ∪K_(1,a_3) ∪K_(1,b) where a_1 + a_2 + a_3 - 1 ≤ b ≤ a_1 + a_2 + a_3 + 1

摘要

A graph G = (V, E) with p vertices and q edges is said to be a skolem mean graph if there exists a function f from the vertex set of G to {1, 2,...,p} such that the induced map f~* from the edge set of G to {2, 3, ...,p} defined by f~*(e = uv) = (f(u) + f(v))/2 if f(u) + f(v) is even and (f(u) + f(v)+1)/2 if f(u) + f(v) is odd, then the resulting edges get distinct labels from the set {2, 3,...,p}. In this paper, we prove that four star graph G = K_(1,a_1) ∪K_(1,a_2) ∪K_(1,a_3) ∪K_(1,b) where a_1 ≤ a_2 ≤ a_3 is a skolem mean graph if a_1 + a_2 + a_3 - 1 ≤ b ≤ a_1 + a_2 + a_3 + 1. (or |b - a_1 - a_2 - a_3| ≤ 1).