TY - MGZN
AU - Balbuena, C.
AU - Dalfo, C.
AU - Martínez, B.
T2 - Discussiones mathematicae. Graph theory
Y1 - 2019
DO - 10.7151/dmgt.2218
UR - https://www.dmgt.uz.zgora.pl/publish/view_pdf.php?ID=4689
AB - A (1, = `)-identifying code in a digraph D is a subset C of vertices of D such that all distinct subsets of vertices of cardinality at most ` have distinct closed in-neighbourhoods within C. In this paper, we give some sufficient conditions for a digraph of minimum in-degree d - = 1 to admit a (1, = `)- identifying code for ` ¿ {d -, d- + 1}. As a corollary, we obtain the result by Laihonen that states that a graph of minimum degree d = 2 and girth at least 7 admits a (1, = d)-identifying code. Moreover, we prove that every 1-in-regular digraph has a (1, = 2)-identifying code if and only if the girth of the digraph is at least 5. We also characterize all the 2-in-regular digraphs admitting a (1, = `)-identifying code for ` ¿ {2, 3}.
TI - Sufficient conditions for a digraph to admit a (1,=l)-identifying code
ER -