K-super cube root cube mean labeling of graphs

Abstract

Consider a graph G with |V (G)| = p and |E(G)| = q and let f : V (G) → {k, k + 1, k + 2, . . . p + q + k − 1}} be an injective function. The induced edge labeling f ∗ for a vertex labeling f is defined by f ∗ (e) = for all e = uv ∈ E(G) is bijective. If f(V (G)) ∪ {f ∗ (e) : e ∈ E(G)} = {k, k + 1, k + 2, . . . , p + q + k − 1}, then f is called a k-super cube root cube mean labeling. If such labeling exists, then G is a k-super cube root cube mean graph. In this paper, I introduce k-super cube root cube mean labeling and prove the existence of this labeling to the graphs viz., triangular snake graph Tn, double triangular snake graph D(Tn), Quadrilateral snake graph Qn, double quadrilateral snake graph D(Qn), alternate triangular snake graph A(Tn), alternate double triangular snake graph AD(Tn), alternate quadrilateral snake graph A(Qn), & alternate double quadrilateral snake graph AD(Qn).