Kings and serfs in oriented graphs

Irredundance and domination in kings graphs

Each king on an n×n chessboard is said to attack its own square and its neighboring squares, i.e., the nine or fewer squares within one move of the king. A set of kings is said to form an irredundant set if each attacks a square attacked by no other king in the set. We prove that the maximum size of an irredundant set of kings is bounded between (n− 1)=3 and n=3, and that the minimum size of a ...

k-Dependence and Domination in Kings Graphs

X iv :m at h/ 06 08 14 0v 1 [ m at h. O C ] 5 A ug 2 00 6 k-Dependence and Domination in Kings Graphs Eugen J. Ionascu, Dan Pritikin, Stephen E. Wright Department of Mathematics, Columbus State University Columbus, GA 31907; ionascu [email protected] Honorific Member of the Romanian Institute of Mathematics “Simion Stoilow” Department of Mathematics and Statistics, Miami University Oxford, OH ...

Medians of Graphs and Kings of Tournaments*

We first prove that for any graph G with a positive vertex weight function w, there exists a graph H with a positive weight function w′ such that w(v) = w′(v) for all vertices v in G and whose w′-median is G. This is a generalization of a previous result for the case in which all weights are 1. The second result is that for any n-tournament T without transmitters, there exists an integer m ≤ 2n...

New skew equienergetic oriented graphs

Let $S(G^{sigma})$ be the skew-adjacency matrix of the oriented graph $G^{sigma}$, which is obtained from a simple undirected graph $G$ by assigning an orientation $sigma$ to each of its edges. The skew energy of an oriented graph $G^{sigma}$ is defined as the sum of absolute values of all eigenvalues of $S(G^{sigma})$. Two oriented graphs are said to be skew equienergetic iftheir skew energies...

Asymptoti ally optimal tree-pa kings in regular graphs