Abstract
The edge H -irregularity strength, e h s Γ , H , of a graph Γ is the smallest integer k , such that Γ has an H -irregular edge k -labeling. In this study, we compute the exact value of edge H -irregularity strength of hexagonal and octagonal grid graphs.
Highlights
E edge k-labeling ζ is called irregular if wtζ(u) ≠ wtζ(v), ∀u≠ v ∈ V(Γ). e irregularity strength of Γ, s(Γ), is the minimum k ∈ Z+, such that there exists an edge irregular k-labeling of Γ. e concept of the irregularity strength of a graph was introduced by Chartrand et al [2]. ere has been a flurry of research work on the irregularity strength in the last few years [3,4,5,6,7,8,9,10,11,12]
An edge k-labeling ζ is called an H-irregular edge k-labeling of the graph Γ that admits H-covering if for every two distinct subgraphs H1 and H2, which are isomorphic to H, wtζ(H1) ≠ wtζ(H2). e edge H-irregularity strength of a graph Γ, ehs(Γ, H), is the smallest integer k, such that Γ has an H-irregular edge k-labeling
Conflicts of Interest e authors declare that they have no conflicts of interest
Summary
E edge irregularity strength of Γ, es(Γ), is the minimum k, such that the graph Γ has an edge irregular k-labeling. Ashraf et al [14] have introduced two new graph parameters, i.e., vertex (edge) H-irregularity strength of a graph. An edge k-labeling ζ is called an H-irregular edge k-labeling of the graph Γ that admits H-covering if for every two distinct subgraphs H1 and H2, which are isomorphic to H, wtζ(H1) ≠ wtζ(H2). Ese networks can be extended in both horizontal and vertical directions, so that the extension in the graphs and networks can be handled and made easy These networks are used especially in communication networks, and the efficiency of the networks may be improved as the weights of the each face have distinct numbers
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