The (2,1)-total labeling number of outerplanar graphs is at most Δ + 2

Toru Hasunuma, Toshimasa Ishii, Hirotaka Ono, Yushi Uno

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)


A (2,1)-total labeling of a graph G is an assignment f from the vertex set V(G) and the edge set E(G) to the set {0,1,...,k} of nonnegative integers such that |f(x) - f(y)| ≥ 2 if x is a vertex and y is an edge incident to x, and |f(x) - f(y)| ≥ 1 if x and y are a pair of adjacent vertices or a pair of adjacent edges, for all x and y in V(G) ∪ E(G). The (2,1)-total labeling number λ2T(G) of G is defined as the minimum k among all possible assignments. In [D. Chen and W. Wang. (2,1)-Total labelling of outerplanar graphs. Discr. Appl. Math. 155 (2007)], it was conjectured that all outerplanar graphs G satisfy λ2T(G) < Δ(G) + 2, where Δ(G) is the maximum degree of G, while they also showed that it is true for G with Δ(G) ≥ 5. In this paper, we solve their conjecture completely, by proving that λ2T(G) ≤ Δ(G) + 2 even in the case of Δ(G) ≤ 4.

Original languageEnglish
Title of host publicationCombinatorial Algorithms - 21st International Workshop, IWOCA 2010, Revised Selected Papers
Number of pages4
Publication statusPublished - 2011
Event21st International Workshop on Combinatorial Algorithms, IWOCA 2010 - London, United Kingdom
Duration: Jul 26 2010Jul 28 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6460 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other21st International Workshop on Combinatorial Algorithms, IWOCA 2010
Country/TerritoryUnited Kingdom

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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