## Abstract

In this paper, we consider a limited version of the well-studied dominating broadcast function of a graph. For a graph G, a function f:V(G)→{0,1,2} is a 2-limited dominating broadcast if for each vertex u in G there exist a vertex v such that f(v)>0 and d_{G}(u,v)≤f(v), where d_{G}(u,v) denotes the distance between u and v in G. The cost of a 2-limited dominating broadcast f is the sum of the function values f(v) summed over all vertices v in G. The 2-limited broadcast domination number of G, denoted by γ_{b,2}(G), is the minimum cost of a 2-limited dominating broadcast in G. We observe that γ_{b,2}(G)≤γ(G), where γ(G) is the domination number of G. A graph is (C_{4},C_{6})-free if it does not contain a 4-cycle or a 6-cycle as an induced subgraph. We prove that if G is a cubic graph of order n that is (C_{4},C_{6})-free, then [Formula presented].

Original language | English |
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Pages (from-to) | 691-706 |

Number of pages | 16 |

Journal | Discrete Applied Mathematics |

Volume | 285 |

DOIs | |

Publication status | Published - 15 Oct 2020 |

## Keywords

- 2-limited dominating broadcast function
- Cubic graphs
- Dominating set

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics