Regresar

Computation of edge C <inf>4</inf>-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 H 1, H 2, …, Ht 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(H i) ϕ(e) ≠ ∑ e∈(Hj) ϕ(e) for every 1 ≤ i < j ≤ t. In this paper, we determine the exact values of ehs(G, C 4) for a grid graph and a generalized prism.