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List graphs and distance-consistent node labelings
Blekinge Tekniska Högskola, Fakulteten för teknikvetenskaper, Institutionen för matematik och naturvetenskap.
Blekinge Tekniska Högskola, Fakulteten för teknikvetenskaper, Institutionen för matematik och naturvetenskap.
2018 (engelsk)Inngår i: Electronic Journal of Graph Theory and Applications, ISSN 2338-2287, Vol. 6, nr 1, s. 152-165Artikkel i tidsskrift (Fagfellevurdert) Published
##### Abstract [en]

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) &lt; 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.

##### sted, utgiver, år, opplag, sider
INST TEKNOLOGI BANDUNG , 2018. Vol. 6, nr 1, s. 152-165
##### Emneord [en]
Extremal combinatorics, Graph distance, Graph labeling
##### Identifikatorer
ISI: 000437328400011Scopus ID: 2-s2.0-85045005282OAI: oai:DiVA.org:bth-16110DiVA, id: diva2:1198941
Tilgjengelig fra: 2018-04-19 Laget: 2018-04-19 Sist oppdatert: 2018-08-20bibliografisk kontrollert

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