Local inclusive distance antimagic coloring of graphs - Hadiputra, Fawwaz Fakhrurrozi; Farhan, Mohammad; Mukayis, Mukayis; Saputro, Suhadi Wido; Maryati, Tita Khalis (Indonesian Journal of Combinatorics, 2024)
For a simple graph G, a bijection f : V(G) → [1,|V (G)|] is called as a local inclusive distance antimagic (LIDA) labeling of G if w(u) ≠ w(v) for every two adjacent vertices u,v ∈ V(G) with w(u) = ∑x∈N [u] f(x). A graph G is said to be local inclusive distance antimagic (LIDA) graph if it admits a LIDA labeling. The function w induced by f also can be seen as a proper vertex coloring of G. The local inclusive distance antimagic (LIDA) chromatic number of G, denoted by χlida(G), is the minimum number of colors taken over all proper vertex colorings induced by LIDA labelings of G. In this paper, we study a LIDA labeling of simple graph. We provide some basic properties of LIDA labeling for any simple graphs. The LIDA chromatic number of certain multipartite graphs, double stars, subdivision of graphs and join product of graphs with K1 are also investigated. We present an upper bound for graphs obtained from subdivision of super edge-magic total graphs. Furthermore, we present some new open problems.