Open Accessk-super cube root cube mean labeling of graphs
Author(s) -
V. Princy Kala
Publication year - 2021
Publication title -
proyecciones
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.226
H-Index - 12
eISSN - 0717-6279
pISSN - 0716-0917
DOI - 10.22199/issn.0717-6279-4258
Subject(s) - combinatorics , quadrilateral , injective function , mathematics , bijection , cube (algebra) , graph , vertex (graph theory) , cube root , discrete mathematics , physics , geometry , finite element method , thermodynamics
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).