﻿ The Italian domatic number of a digraph

The Italian domatic number of a digraph

چکیده

An {em Italian dominating function} on a digraph \$D\$ with vertex set \$V(D)\$ is defined as a function\$fcolon V(D)to {0, 1, 2}\$ such that every vertex \$vin V(D)\$ with \$f(v)=0\$ has at least two in-neighborsassigned 1 under \$f\$ or one in-neighbor \$w\$ with \$f(w)=2\$. A set \${f_1,f_2,ldots,f_d}\$ of distinctItalian dominating functions on \$D\$ with the property that \$sum_{i=1}^d f_i(v)le 2\$ for each \$vin V(D)\$,is called an {em Italian dominating family} (of functions) on \$D\$. The maximum number of functions in anItalian 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 sharpbounds for \$d_{I}(D)\$. In addition, we determine the Italian domatic number of some digraphs.

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عنوان ژورنال:

دوره 4  شماره 1

صفحات  61- 70

تاریخ انتشار 2019-06-01

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