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- W4386523714 abstract "Let G = ( V , E ) be a graph and the deficiency of G be def( G ) = ∑ v ∈V(G)(Δ(G)−d G ( v )), where d G ( v ) is the degree of a vertex v in G . A vertex coloring φ:V(G)→{1,2,...,Δ(G)+1} is called conformable if the number of color classes (including empty color classes) of parity different from that of | V ( G )| is at most def ( G ). A general characterization for conformable graphs is unknown. Conformability plays a key role in the total chromatic number theory. It is known that if G is Type 1 , then G is conformable. In this paper, we prove that if G is k -regular and Class 1 , then L ( G ) is conformable. As an application of this statement we establish that the line graph of complete graph L ( K n ) is conformable, which is a positive evidence towards the Vignesh et al. ’s conjecture that L ( K n ) is Type 1 ." @default.
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- W4386523714 date "2023-09-01" @default.
- W4386523714 modified "2023-10-09" @default.
- W4386523714 title "On the conformability of regular line graphs" @default.
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- W4386523714 doi "https://doi.org/10.1051/ro/2023140" @default.
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