Computation of edge C₄-irregularity strength of Cartesian product of graphs

Abstract

If every edge in the graph G is also an edge of a subgraph of G isomorphic to a given graph H we say that the graph G admits an H-covering. Let G be a graph admitting an H-covering and let H₁, H₂, … , H_t be all subgraphs in G isomorphic to H. The edge H-irregularity strength of a graph G is the smallest integer k for which one can find a mapping ϕ : E(G) → {1, 2, … , k} such that ∑_e∈E(Hi)ϕ(e) ≠ ∑_e∈(Hj)ϕ(e) for every 1 ≤ i < j ≤ t.

In this paper, we determine the exact values of ehs(G, C₄) for a grid graph and a generalized prism.

Subject Classification:

• 05C78
• 05C70

Keywords:

• H-irregular edge labeling
• Edge H-irregularity strength
• Grid graph
• Generalized prism