## Abstract

In this paper, we define the signed total domatic number of a graph in an analogous way to that of the fractional domatic number defined by Rail (A fractional version of domatic number. Congr. Numer. 74 (1990), 100-106). A function f: V(G) → {-1, 1} defined on the vertices of a graph G is a signed total dominating function if the sum of its function values over any open neighborhood is at least one. A set {f_{1}, f_{d}} of signed total dominating functions on G such that ∑_{i=1}^{d} fi(v) ≤ 1 for each vertex v ∈ V(G) is called a signed total dominating family of functions on G. The signed total domatic number of G is the maximum number of functions in a signed total dominating family of G. In this paper we investigate the signed total domatic number for special classes of graphs.

Original language | English |
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Pages (from-to) | 277-288 |

Number of pages | 12 |

Journal | Ars Combinatoria |

Volume | 79 |

Publication status | Published - Apr 2006 |

Externally published | Yes |

## Keywords

- AMS subject classification: 05C69
- Signed total domatic number
- Signed total dominating function

## ASJC Scopus subject areas

- General Mathematics