Related papers: Kings and serfs in oriented graphs
A tournament is a complete directed graph. A king in a tournament is a vertex v such that every other vertex is reachable from v via a path of length at most 2. It is well known that every tournament has at least one king, one of which is a…
In adversarial networks, edges correspond to negative interactions such as competition or dominance. We introduce a new type of node called a low-key leader in adversarial networks, distinguished by contrasting the centrality measures of…
The paper presents a hierarchical Bayesian model for simultaneous inference of tournament graphs and informant error. From multiple informant reports or measurement instrument outputs, the model estimates the structure of a criterion (i.e.,…
\textsc{Cops and Robber} is one of the most studied two-player pursuit-evasion games played on graphs, where multiple \textit{cops}, controlled by one player, pursue a single \textit{robber}. The main parameter of interest is the…
We initiate a general study of what we call orientation completion problems. For a fixed class C of oriented graphs, the orientation completion problem asks whether a given partially oriented graph P can be completed to an oriented graph in…
Strongly chordal digraphs are included in the class of chordal digraphs and generalize strongly chordal graphs and chordal bipartite graphs. They are the digraphs that admit a linear ordering of its vertex set for which their adjacency…
For integers $k \geq 2$ and $n \geq k+1$, we prove the following: If $n\cdot k$ is even, there is a connected $k$-regular graph on $n$ vertices. If $n\cdot k$ is odd, there is a connected nearly $k$-regular graph on $n$ vertices.
We characterize the equivalence and the weak equivalence of Cayley graphs for a finite group $\C{A}$. Using these characterizations, we find enumeration formulae of the equivalence classes and weak equivalence classes of Cayley graphs. As…
An undirected graph is said to be cordial if there is a friendly (0,1)-labeling of the vertices that induces a friendly (0,1)-labeling of the edges. An undirected graph $G$ is said to be $(2,3)$-orientable if there exists a friendly…
Signed graphs have been introduced to enrich graph structures expressing relationships between persons or general social entities, introducing edge signs to reflect the nature of the relationship, e.g., friendship or enmity. Independently,…
We give some new characterizations of almost weak Dunford-Pettis operators and we investigate their relationship with weak Dunford-Pettis operators.
The niche graph of a digraph $D$ has $V(D)$ as the vertex set and an edge $uv$ if and only if $(u,w) \in A(D)$ and $(v,w) \in A(D)$, or $(w,u) \in A(D)$ and $(w,v) \in A(D)$ for some $w \in V(D)$. The notion of niche graph was introduced by…
The graph $G$ is said to be strongly regular with parameters $(n,k,\lambda,\mu)$ if the following conditions hold: (1) each vertex has $k$ neighbours; (2) any two adjacent vertices of $G$ have $\lambda$ common neighbours; (3) any two…
We characterize the tournaments that are dominance graphs of sets of (unfair) coins in which each coin displays its larger side with greater probability. The class of these tournaments coincides with the class of tournaments whose vertices…
The orientation completion problem for a class of oriented graphs asks whether a given partially oriented graph can be completed to an oriented graph in the class by orienting the unoriented edges of the partially oriented graph.…
Ranking the participants of a tournament has applications in voting, paired comparisons analysis, sports and other domains. In this paper we introduce bipartite tournaments, which model situations in which two different kinds of entity…
The concept of power among players can be expressed as a combination of their utilities. A player who obeys another takes into account the utility of the dominant one. Technically it is a matter of superimposing some weighted sum or product…
In this thesis we consider ordered graphs (that is, graphs with a fixed linear ordering on their vertices). We summarize and further investigations on the number of edges an ordered graph may have while avoiding a fixed forbidden ordered…
It is introduced the concept of a quasi-king space, which is a natural generalisation of a king space. In the realm of suborderable spaces, king spaces are precisely the compact spaces, so are the quasi-king spaces. In contrast, quasi-king…
In this paper, we study the signed domination numbers of graphs and present new sharp lower and upper bounds for this parameter. As an example, we present a lower bound on signed domination number of trees in terms of the order, leaves and…