| Title: |
Lower Bounds on the Distance Domination Number of a Graph |
| Authors: |
Davila, Randy Ryan; Fast, Caleb; Henning, Michael; Kenter, Franklin |
| Source: |
Contributions to Discrete Mathematics; Vol. 12 No. 2 (2017) ; 1715-0868 ; 10.55016/ojs/cdm.v12i2 |
| Publisher Information: |
Faculty of Science, University of Calgary |
| Publication Year: |
2017 |
| Collection: |
University of Calgary Journal Hosting |
| Subject Terms: |
Mathematics; Discrete Mathematics; Graph Theory; Domination Number |
| Description: |
For an integer $k \ge 1$, a (distance) $k$-dominating set of a connected graph $G$ is a set $S$ of vertices of $G$ such that every vertex of $V(G) \setminus S$ is at distance at most~$k$ from some vertex of $S$. The $k$-domination number, $\gamma_k(G)$, of $G$ is the minimum cardinality of a $k$-dominating set of $G$. In this paper, we establish lower bounds on the $k$-domination number of a graph in terms of its diameter, radius, and girth. We prove that for connected graphs $G$ and $H$, $\gamma_k(G \times H) \ge \gamma_k(G) + \gamma_k(H) -1$, where $G \times H$ denotes the direct product of $G$ and $H$. |
| Document Type: |
article in journal/newspaper |
| File Description: |
application/pdf |
| Language: |
English |
| Relation: |
https://cdm.ucalgary.ca/article/view/62487/46806; https://cdm.ucalgary.ca/article/view/62487 |
| DOI: |
10.55016/ojs/cdm.v12i2.62487 |
| Availability: |
https://cdm.ucalgary.ca/article/view/62487; https://doi.org/10.55016/ojs/cdm.v12i2.62487 |
| Rights: |
Copyright (c) 2017 Contributions to Discrete Mathematics |
| Accession Number: |
edsbas.1CF09785 |
| Database: |
BASE |