-циклические орграфы
Score lists of oriented tripartite graphs.
Segments of score sequences.
Self-diclique circulant digraphs
We study a particular digraph dynamical system, the so called digraph diclique operator. Dicliques have frequently appeared in the literature the last years in connection with the construction and analysis of different types of networks, for instance biochemical, neural, ecological, sociological and computer networks among others. Let be a reflexive digraph (or network). Consider and (not necessarily disjoint) nonempty subsets of vertices (or nodes) of . A disimplex of is the subdigraph...
Semidomatic and total semidomatic numbers of directed graphs
Certain numerical invariants of directed graphs, analogous to the domatic number and to the total domatic number of an undirected graph, are introduced and studied.
Semidomatic numbers of directed graphs
Sharp Upper Bounds on the Signless Laplacian Spectral Radius of Strongly Connected Digraphs
Let G = (V (G),E(G)) be a simple strongly connected digraph and q(G) be the signless Laplacian spectral radius of G. For any vertex vi ∈ V (G), let d+i denote the outdegree of vi, m+i denote the average 2-outdegree of vi, and N+i denote the set of out-neighbors of vi. In this paper, we prove that: (1) (1) q(G) = d+1 +d+2 , (d+1 ≠ d+2) if and only if G is a star digraph [...] ,where d+1, d+2 are the maximum and the second maximum outdegree, respectively [...] is the digraph on n vertices obtained...
Short certificates for tournaments.
Short cycles in digraphs with local average outdegree at least two.
Short score certificates for upset tournaments.
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.