## Abstract

Let (Formula presented.) be an integer, and let (Formula presented.) be a finite and simple graph with vertex set (Formula presented.). A signed Roman (Formula presented.)-dominating function (SRkDF) on a graph (Formula presented.) is a function (Formula presented.) satisfying the conditions that (i)(Formula presented.) for each vertex (Formula presented.), where (Formula presented.) is the closed neighborhood of (Formula presented.), and (ii) every vertex(Formula presented.) for which (Formula presented.) is adjacent to at least one vertex (Formula presented.) for which (Formula presented.). The weight of an SRkDF(Formula presented.) is (Formula presented.). The signed Roman (Formula presented.)-domination number (Formula presented.) of (Formula presented.) is the minimum weight of an (Formula presented.) on (Formula presented.). In this paper we initiate the study of the signed Roman (Formula presented.)-domination number of graphs, and we present different bounds on (Formula presented.). In addition, we determine the signed Roman $$k$$k-domination number of some classes of graphs. Some of our results are extensions of well-known properties of the signed Roman domination number (Formula presented.), introduced and investigated by Ahangar et al. (J Comb Optim doi:10.1007/s10878-012-9500-0, 2014).

Original language | English |
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Pages (from-to) | 175-190 |

Number of pages | 16 |

Journal | Graphs and Combinatorics |

Volume | 32 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2016 |

## Keywords

- Signed Roman k-dominating function
- Signed Roman k-domination number

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics