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On local edge antimagic chromatic number of graphs
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Let G=(V,E) be a graph of order p and size q having no isolated vertices. A bijection f from V to {1,2,3,...,p} is called a local edge antimagic labeling if for any two adjacent edges e=uv and e'=vw of G, we have w(e) is not equal to w (e'), where the edge weight w(e=uv)=f(u)+f(v) and w(e')=f(v)+f(w). A graph G is local edge antimagic if G has a local edge antimagic labeling. The local edge antimagic chromatic number is defined to be the minimum number of colors taken over all colorings of G induced by local edge antimagic labelings of G. In this paper, we determine the local edge antimagic chromatic number for a friendship graph, wheel graph, fan graph, helm graph, flower graph, and closed helm.
Title: On local edge antimagic chromatic number of graphs
Description:
Let G=(V,E) be a graph of order p and size q having no isolated vertices.
A bijection f from V to {1,2,3,.
,p} is called a local edge antimagic labeling if for any two adjacent edges e=uv and e'=vw of G, we have w(e) is not equal to w (e'), where the edge weight w(e=uv)=f(u)+f(v) and w(e')=f(v)+f(w).
A graph G is local edge antimagic if G has a local edge antimagic labeling.
The local edge antimagic chromatic number is defined to be the minimum number of colors taken over all colorings of G induced by local edge antimagic labelings of G.
In this paper, we determine the local edge antimagic chromatic number for a friendship graph, wheel graph, fan graph, helm graph, flower graph, and closed helm.
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