On local super h-decomposition antimagic total coloring of graphs

Abstract

The writer introduces of local super H−decomposition antimagic total coloring of G. Let G(V, E) be a graph with vertex set V and edge set E. A bijection f : V(G) ∪ E(G) → {1, 2, 3, …, |V(G)| + |E(G)|} is called a local H−decomposition antimagic total labeling for any two adjacent subgraph H1 and H2, wt(H1) ≠ wt(H2), where wt(H) = ∑v∈ V(H)f(v) + ∑e∈ E(H)f(e). Thus, any local super H−decomposition antimagic total labeling induces a proper subgraph coloring of G if each subgraph H is assigned by color wt(H). A coloring graph of local super H-decomposition antimagic total coloring is an assignment of colors minimum number. The colors minimum number of graphs namely is chromatic number, denoted by γlaH(G). In this paper, the writer studies the local super H−decomposition antimagic total coloring of graphs namely path graph, cycle graph, prims graph, and jahangir graph.