Let G be a finite simple cubic graph, not necessarily connected, and let S_2(G) be obtained by subdividing every edge of G twice. Li (2025) developed general constructions for antimagic labelings of repeated subdivisions, but the cubic case G(3) = S_2(G) is not covered by those methods. Our first proof constructs an ed...
A labeling of a connected graph $G$ on $n$ vertices is a bijection $c:V(G)\to\{1,\dots,n\}$; writing $c(u,v)=|c(u)-c(v)|$, a vertex $u$ is list-distance consistent if $d(u,v)<d(u,w)$ implies $c(u,v)\le c(u,w)$ for all $v,w$. The maximum number of such vertices over all labelings is the list-distance consistency ldc$(G)...
Fei-Huang Chang, Ma-Lian Chia, David Kuo et al.· 0 citations
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