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List graphs and dis...
List graphs and distance-consistent node labelings
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- Lennerstad, Håkan (author)
- Blekinge Tekniska Högskola,Institutionen för matematik och naturvetenskap
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- Eriksson, Mattias (author)
- Blekinge Tekniska Högskola,Institutionen för matematik och naturvetenskap
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(creator_code:org_t)
- 2018-04-03
- 2018
- English.
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In: Electronic Journal of Graph Theory and Applications. - : INST TEKNOLOGI BANDUNG. - 2338-2287. ; 6:1, s. 152-165
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Abstract
Subject headings
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- 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.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Keyword
- Extremal combinatorics
- Graph distance
- Graph labeling
Publication and Content Type
- ref (subject category)
- art (subject category)
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