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

Toru Hasunuma, Toshimasa Ishii, Hirotaka Ono, Yushi Uno

研究成果: 書籍/レポート タイプへの寄稿会議への寄与

3 被引用数 (Scopus)

抄録

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.

本文言語英語
ホスト出版物のタイトルCombinatorial Algorithms - 21st International Workshop, IWOCA 2010, Revised Selected Papers
ページ103-106
ページ数4
DOI
出版ステータス出版済み - 2011
イベント21st International Workshop on Combinatorial Algorithms, IWOCA 2010 - London, 英国
継続期間: 7月 26 20107月 28 2010

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
6460 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

その他

その他21st International Workshop on Combinatorial Algorithms, IWOCA 2010
国/地域英国
CityLondon
Period7/26/107/28/10

!!!All Science Journal Classification (ASJC) codes

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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