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 T_n, double triangular snake graph D(T_n), Quadrilateral snake graph Q_n, double quadrilateral snake graph D(Q_n), alternate triangular snake graph A(T_n), alternate double triangular snake graph AD(Tn), alternate quadrilateral snake graph A(Q_n), & alternate double quadrilateral snake graph AD(Q_n).