Antimagicness of $mC_n$ -Path and Its Disjoint Union

Abstract

Let M = (V (M), E(M)) be a simple graph with finite vertices and edges. An N-covering of M is a family {N 1 , N 2 ,. .. , N α } of subgraphs of M isomorphic to N such that every edge in E(M) belongs to N l , for some l, l ∈ {1, 2,. .. , α}. Such a graph is a (c, d)-N-antimagic if ∃ a bijection ψ : V M ∪E M → {1, 2,. .. , |V M |+|E M |} such that for all N l ∼ = N , {wt ψ (N l)} = {c, c+d,. .. , c+(α −1)d}. For ψ(V (M)) = {1, 2, 3,. .. , |V (M)|}, the labeling ψ would be super (c, d)-N-antimagic and for d = 0 it would be N-supermagic. In this manuscript, we investigated that mC n-path has super (c, d)-C n-antimagic labeling for differences d ∈ {0, 1,. .. , 5} and extend the result for C n-supermagic labeling of disjoint union of isomorphic copies of mC n-path. INDEX TERMS Block cut-vertex graph, mC n-path, disjoint union of mC n-path, super (c, d)-C n-antimagic.

H-Coverings of Path-Amalgamated Ladders and Fans

“…From equations (14) and (15), it is clear the labeling ϕ is a total labeling, since ϕ is a bijection between the integers 1, 2, . .…”

“…Susanto [7] derived bound for cycle-antimagic labeling of disjoint union of cycles. Recent results on H-antimagic labeling of graphs can be seen in [8][9][10][11][12][13][14]. Also, in [12], Baca et al discussed the tree-antimagicness of disconnected graphs.…”

Radio Labeling for Strong Product K3 ⊠ Pn

“…Many real life problems: radar codes, missile guidance coding, crystallography, signal processing, finding a molecular structure and channel assignment over a wireless network have been solved by the aid of graph theory and graph labeling. Different types of labeling and their results have been formulated and designed: graceful, harmonious, magic, VAT, EAT, cordial, prime, coprime, radio, H-antimagic and complex addition labeling are some of these [1]- [8].…”