Sign patterns that require or allow power-positivity.
Signed degree sets in signed graphs
The set of distinct signed degrees of the vertices in a signed graph is called its signed degree set. In this paper, we prove that every non-empty set of positive (negative) integers is the signed degree set of some connected signed graph and determine the smallest possible order for such a signed graph. We also prove that every non-empty set of integers is the signed degree set of some connected signed graph.
Signed domination and signed domatic numbers of digraphs
Let D be a finite and simple digraph with the vertex set V(D), and let f:V(D) → -1,1 be a two-valued function. If for each v ∈ V(D), where N¯[v] consists of v and all vertices of D from which arcs go into v, then f is a signed dominating function on D. The sum f(V(D)) is called the weight w(f) of f. The minimum of weights w(f), taken over all signed dominating functions f on D, is the signed domination number of D. A set of signed dominating functions on D with the property that for each...
Signed domination numbers of directed graphs
The concept of signed domination number of an undirected graph (introduced by J. E. Dunbar, S. T. Hedetniemi, M. A. Henning and P. J. Slater) is transferred to directed graphs. Exact values are found for particular types of tournaments. It is proved that for digraphs with a directed Hamiltonian cycle the signed domination number may be arbitrarily small.
Signed total -domatic numbers of digraphs
Signed total -domination numbers of directed graphs.
Signed Total Roman Domination in Digraphs
Let D be a finite and simple digraph with vertex set V (D). A signed total Roman dominating function (STRDF) on a digraph D is a function f : V (D) → {−1, 1, 2} satisfying the conditions that (i) ∑x∈N−(v) f(x) ≥ 1 for each v ∈ V (D), where N−(v) consists of all vertices of D from which arcs go into v, and (ii) every vertex u for which f(u) = −1 has an inner neighbor v for which f(v) = 2. The weight of an STRDF f is w(f) = ∑v∈V (D) f(v). The signed total Roman domination number γstR(D) of D is the...
Simple score sequences in oriented graphs.
Simultaneous representations in discrete structures
Singular values of tournament matrices.
Small directed graphs as neighbourhood graphs
Small forbidden configurations. II.
Solutions and kernels of a directed graph
Solutions de tournois : un spicilège
L'article passe en revue quelques Solutions de Tournois (correspondances de choix définies sur les tournois). On compare ces solutions entre elles, et on mentionne certaines de leurs propriétés.
Some algebraic aspects of tournament theory
Some combinatorial problems, connected with product-isomorphisms of binary relations
Some new good characterizations for directed graphs
Some properties complementary to Brualdi-Li matrices
In this paper we derive new properties complementary to an Brualdi-Li tournament matrix . We show that has exactly one positive real eigenvalue and one negative real eigenvalue and, as a by-product, reprove that every Brualdi-Li matrix has distinct eigenvalues. We then bound the partial sums of the real parts and the imaginary parts of its eigenvalues. The inverse of is also determined. Related results obtained in previous articles are proven to be corollaries.
Some remarks about digraphs with nonisomorphic - or -neighbourhoods
Some Remarks On The Structure Of Strong K-Transitive Digraphs
A digraph D is k-transitive if the existence of a directed path (v0, v1, . . . , vk), of length k implies that (v0, vk) ∈ A(D). Clearly, a 2-transitive digraph is a transitive digraph in the usual sense. Transitive digraphs have been characterized as compositions of complete digraphs on an acyclic transitive digraph. Also, strong 3 and 4-transitive digraphs have been characterized. In this work we analyze the structure of strong k-transitive digraphs having a cycle of length at least k. We show...