On modulo local antimagic chromatic number of graphs

Abstract

An edge labeling of a connected (p, q) -graph G = (V, E) of order p and size q is a modulo local antimagic labeling if it is a bijection π : E → {1, … ,q} such that for any pair of adjacent vertices u and v, π +(u) ≠ π +(v), where the induced vertex label π +(u) = ∑π(e)(mod p), with e ranging over all the edges incident to u. The modulo local antimagic chromatic number of G, denoted πla (G), is the minimum number of distinct induced vertex labels over all modulo local antimagic labelings of G. In this paper, we shall study the relationship among chromatic number, local antimagic chromatic number and modulo local antimagic chromatic number of graphs. Many open problems for further research are also presented.