List graphs and distance-consistent node labelings

Lennerstad, HåkanBlekinge Tekniska Högskola,Institutionen för matematik och naturvetenskap (author)

In this paper we consider node labelings c of an undirected connected graph G = (V,E) with labels (1, 2, ...,|V|), which induce a list distance c(u, v) = |c(v) - c(u)| besides the usual graph distance d(u, v). Our main aim is to find a labeling c so c(u; v) is as close to d(u, v) as possible. For any graph we specify algorithms to find a distance-consistent labeling, which is a labeling c that minimize Σ u,vεV (c(u, v) - d(u, v))2. Such labeliings may provide structure for very large graphs. Furthermore, we define a labeling c fulfilling d(u1, v1) < d(u2, v2) ) c(u1, v1) ⇒ c(u2, v2) for all node pairs u1; v1 and u2; v2 as a list labeling, and a graph that has a list labeling is a list graph. We prove that list graphs exist for all n = |V| and all k = |E|: n - 1 ≤ k ≤ n(n - 1)/2, and establish basic properties. List graphs are Hamiltonian, and show weak versions of properties of path graphs. © 2018 Indonesian Combinatorics Society.

Eriksson, MattiasBlekinge Tekniska Högskola,Institutionen för matematik och naturvetenskap(Swepub:bth)meo (author)
Blekinge Tekniska HögskolaInstitutionen för matematik och naturvetenskap (creator_code:org_t)

In:Electronic Journal of Graph Theory and Applications: INST TEKNOLOGI BANDUNG6:1, s. 152-1652338-2287

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