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The Local Antimagic Total Chromatic Number of Some Wheel-Related Graphs

Authors: Xue Yang; Hong Bian; Haizheng Yu; Dandan Liu;

The Local Antimagic Total Chromatic Number of Some Wheel-Related Graphs

Abstract

Let G=(V,E) be a connected graph with |V|=n and |E|=m. A bijection f:V(G)∪E(G)→{1,2,⋯,n+m} is called local antimagic total labeling if, for any two adjacent vertices u and v, ωt(u)≠ωt(v), where ωt(u)=f(u)+∑e∈E(u)f(e), and E(u) is the set of edges incident to u. Thus, any local antimagic total labeling induces a proper coloring of G, where the vertex x in G is assigned the color ωt(x). The local antimagic total chromatic number, denoted by χlat(G), is the minimum number of colors taken over all colorings induced by local antimagic total labelings of G. In this paper, we present the local antimagic total chromatic numbers of some wheel-related graphs, such as the fan graph Fn, the bowknot graph Bn,n, the Dutch windmill graph D4n, the analogous Dutch graph AD4n and the flower graph Fn.

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Keywords

wheel-related graphs, QA1-939, local antimagic total labeling, local antimagic total chromatic number, Mathematics, local antimagic total labeling; local antimagic total chromatic number; wheel-related graphs

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
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Average
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