Open this publication in new window or tab >>2018 (English)In: Electronic Journal of Graph Theory and Applications, ISSN 2338-2287, Vol. 6, no 1, p. 152-165Article in journal (Refereed) 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) < 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.
Place, publisher, year, edition, pages
INST TEKNOLOGI BANDUNG, 2018
Keywords
Extremal combinatorics, Graph distance, Graph labeling
National Category
Mathematics
Identifiers
urn:nbn:se:bth-16110 (URN)10.5614/ejgta.2018.6.1.11 (DOI)000437328400011 ()2-s2.0-85045005282 (Scopus ID)
2018-04-192018-04-192018-08-20Bibliographically approved