Location-domatic number of a graph

Bohdan Zelinka

Displaying similar documents to “Location-domatic number of a graph”

Point-set domatic numbers of graphs

Bohdan Zelinka (1999)

Mathematica Bohemica

Similarity:

A subset $D$ of the vertex set $V (G)$ of a graph $G$ is called point-set dominating, if for each subset $S \subseteq V (G) - D$ there exists a vertex $v \in D$ such that the subgraph of $G$ induced by $S \cup {v}$ is connected. The maximum number of classes of a partition of $V (G)$ , all of whose classes are point-set dominating sets, is the point-set domatic number $d_{p} (G)$ of $G$ . Its basic properties are studied in the paper.

Induced-paired domatic numbers of graphs

Bohdan Zelinka (2002)

Mathematica Bohemica

Similarity:

A subset $D$ of the vertex set $V (G)$ of a graph $G$ is called dominating in $G$ , if each vertex of $G$ either is in $D$ , or is adjacent to a vertex of $D$ . If moreover the subgraph $< D >$ of $G$ induced by $D$ is regular of degree 1, then $D$ is called an induced-paired dominating set in $G$ . A partition of $V (G)$ , each of whose classes is an induced-paired dominating set in $G$ , is called an induced-paired domatic partition of $G$ . The maximum number of classes of an induced-paired domatic partition of $G$ is the induced-paired...

Stratidistance in stratified graphs

Gary Chartrand, Heather Gavlas, Michael A. Henning, Reza Rashidi (1997)

Mathematica Bohemica

Similarity:

A graph $G$ is a stratified graph if its vertex set is partitioned into classes (each of which is a stratum or a color class). A stratified graph with $k$ strata is $k$ -stratified. If $G$ is a connected $k$ -stratified graph with strata $S_{i}$ $(1 \leq i \leq k)$ where the vertices of $S_{i}$ are colored $X_{i}$ $(1 \leq i \leq k)$ , then the $X_{i}$ -proximity $ρ_{X_{i}} (v)$ of a vertex $v$ of $G$ is the distance between $v$ and a vertex of $S_{i}$ closest to $v$ . The strati-eccentricity $s e (v)$ of $v$ is $max {ρ_{X_{i}} (v) ∣ 1 \leq i \leq k}$ . The minimum strati-eccentricity over all vertices...