1 research outputs found
The signed (k,k) -domatic number of digraphs
et be a finite and simple digraph with vertex set , and
let be a two-valued function. If is an integer and for each , where consists of and all vertices of from
which arcs go into , then is a signed -dominating
function on . A set of distinct signed
-dominating functions on with the property that
for each , is called a signed
-dominating family (of functions) on . The maximum
number of functions in a signed -dominating family on
is the signed -domatic number on , denoted by
.
In this paper, we initiate the study of the signed -domatic
number of digraphs, and we present different bounds on
. Some of our results are extensions of well-known
properties of the signed domatic number of
digraphs as well as the signed -domatic number
of graphs