2-Rainbow Domination of the Circulant Graph C(n;{1,3})

DOI

10.2991/tmcm-15.2015.31How to use a DOI?

Keywords

the Circulant graph; rainbow domination; -rainbow domination number

Abstract

Let G be a graph where for each vertex, a subset of a set of K colors is assigned. If for each vertex to which an empty set is assigned, its neighborhood contains all K colors, then such an assignment is called a K-rainbow dominating function of G. The corresponding invariant rrk(G), which is the minimum sum of the cardinalities of the subsets assigned by a K-rainbow dominating function of G, is called the K-rainbow domination number of G. In this paper, we study the 2-rainbow domination number of the Circulant graph C(n,{1,3}), and we show that rr2(C(n;{1,3}))=2[n/5]+a, where a=0 for n=0(mod 5),a=1 for n=1,2 (mod 5) and a=2 for n=3,4 (mod 5).

Copyright

© 2015, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Xueliang Fu
AU  - Xiaofeng Wu
AU  - Gaifang Dong
AU  - Honghui Li
AU  - William Guo
PY  - 2015/11
DA  - 2015/11
TI  - 2-Rainbow Domination of the Circulant Graph C(n;{1,3})
BT  - Proceedings of the 2015 International Conference on Test, Measurement and Computational Methods
PB  - Atlantis Press
SP  - 123
EP  - 129
SN  - 2352-538X
UR  - https://doi.org/10.2991/tmcm-15.2015.31
DO  - 10.2991/tmcm-15.2015.31
ID  - Fu2015/11
ER  -