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On The Local Edge Antimagic Coloring of Comb Product Graphs

Last modified: 2017-07-05

#### Abstract

All graph in this paper are finite, simple and connected graph. Let $G(V,E)$ be a graph of vertex set $V$ and edge set $E$. A bijection $f:V(G)\longrightarrow \{1,2,3,...,|V(G)|\}$ is called a local edge antimagic labeling if for any two adjacent edges $e_1$ and $e_2$, $w(e_1)\neq w(e_2)$, where for $e=uv\in G$, $w(e)=f(u)+f(v)$. Thus, any local edge antimagic labeling induces a properedge coloring of G if each edge $e$ is assigned the color $w(e)$. The local edge antimagic chromatic number $\gamma_{lae}(G)$ is the minimum number of colors taken over all colorings induced by local edge antimagic labelings of $G$. In this paper we initiate to study the existence of local edge antimagic coloring of some special graphs. We also analyse the lower bound of its local edge antimagic chromatic number. In this Paper, we determine the local edge antimagic coloring of comb product graphs.