Rainbow connection of bridgeless outerplanar graphs with small diameters

Xingchao Deng; He Song; Guifu Su; Weihua Yang

Rainbow connection of bridgeless outerplanar graphs with small diameters

Combinatorics 2016-09-09 v1

Authors: Xingchao Deng , He Song , Guifu Su , Weihua Yang

Abstract

In this paper, we investigate rainbow connection number $rc(G)$ of bridgeless outerplanar graphs $G$ with diameter 2 or 3. We proved the following results: If $G$ has diameter $2,$ then $rc(G)=3$ for fan graphs $F_{n}$ with $n\geq 7$ or $C_5,$ otherwise $rc(G)=2;$ if $G$ has diameter $3,$ then $rc(G)\leq 4$ and the bound is sharp.

Keywords

rainbow connection number bridgeless outerplanar graphs graph diameter fan graphs graph theory

Cite

@article{arxiv.1609.02351,
  title  = {Rainbow connection of bridgeless outerplanar graphs with small diameters},
  author = {Xingchao Deng and He Song and Guifu Su and Weihua Yang},
  journal= {arXiv preprint arXiv:1609.02351},
  year   = {2016}
}

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9 pages,12 figures

Rainbow connection of bridgeless outerplanar graphs with small diameters

Abstract

Keywords

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