The Italian domatic number of a digraph
| Autor: | L.Volkmann |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Communications in Combinatorics and Optimization, Vol 4, Iss 1, Pp 61-70 (2019) |
| Druh dokumentu: | article |
| ISSN: | 2538-2128 2538-2136 |
| DOI: | 10.22049/CCO.2019.26360.1102 |
| Popis: | An {\em Italian dominating function} on a digraph $D$ with vertex set $V(D)$ is defined as a function $f\colon V(D)\to \{0, 1, 2\}$ such that every vertex $v\in V(D)$ with $f(v)=0$ has at least two in-neighbors assigned 1 under $f$ or one in-neighbor $w$ with $f(w)=2$. A set $\{f_1,f_2,\ldots,f_d\}$ of distinct Italian dominating functions on $D$ with the property that $\sum_{i=1}^d f_i(v)\le 2$ for each $v\in V(D)$, is called an {\em Italian dominating family} (of functions) on $D$. The maximum number of functions in an Italian dominating family on $D$ is the {\em Italian domatic number} of $D$, denoted by $d_{I}(D)$. In this paper we initiate the study of the Italian domatic number in digraphs, and we present some sharp bounds for $d_{I}(D)$. In addition, we determine the Italian domatic number of some digraphs. |
| Databáze: | Directory of Open Access Journals |
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