Abstract
Let G = (V, E) be a connected graph with |V|= n and |E|= m. A bijection f : E → {1, 2, … , m} is called a local antimagic lableing if for any two adjacent vertices u and v, w(u) ≠ w(v), where w(u)= ∑ e ϵE(u) f (e) and E(u) is the set of edges incident to u. Thus any local antimagic labeling induces a proper vertex coloring of G where the vertex v is assigned the color w(v). The local antimagic chromatic number χla (G) is the minimum number of colors taken over all colorings induced by local antimagic labelings of G. In this paper we determine the local antimagic chromatic number of several families of trees.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have