R -Domination in Graphs-Reference-Cited by-同舟云学术

R -Domination in Graphs

Published:1976-07 Issue:3 Volume:23 Page:446-450
ISSN:0004-5411
Container-title:Journal of the ACM
language:en
Short-container-title:J. ACM

Author:

Slater Peter J.¹

Affiliation:

1. Applied Mathematics Division 5121, Sandia Laboratories, Albuquerque, NM

Abstract

The problem of finding a minimum k -basis of graph G is that of selecting as small a set B of vertices as possible such that every vertex of G is at distance k or less from some vertex in B . Cockayne, Goodman, and Hedetniemi previously developed a linear algorithm to find a minimum 1-basis (a minimum dominating set) when G is a tree. In this paper the k -basis problem is placed in a more general setting, and a linear algorithm is presented that solves the problem for any forest.

Publisher

Association for Computing Machinery (ACM)

Subject

Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software

Link

https://dl.acm.org/doi/pdf/10.1145/321958.321964

Reference5 articles.

1. com.atypon.pdfplus.internal.model.plusxml.impl.AuthorGroup@3eca26f6 S T A hnear algomthm for the dommatmn number of a tree Submitted for pubhcatlon COCKAYNE E J GOODMAN S E AND HEDETNIEMI S T A hnear algomthm for the dommatmn number of a tree Submitted for pubhcatlon

2. com.atypon.pdfplus.internal.model.plusxml.impl.AuthorGroup@300dcf5f S T Dominating part~tmns of graphs To appear COCKAYNE E J AND HEDETNIEMI S T Dominating part~tmns of graphs To appear

3. com.atypon.pdfplus.internal.model.plusxml.impl.AuthorGroup@34324d86 C Introductmn to Comb~natorml Mathematics McGraw-Hill New York 1968 LIU C Introductmn to Comb~natorml Mathematics McGraw-Hill New York 1968

4. com.atypon.pdfplus.internal.model.plusxml.impl.AuthorGroup@1e22a022 O Theory of Graphs Amer Math Soc Colloqumm Pub Vol XXXVIII Amer Math Soc Providence Rhode Island 1962 ORE O Theory of Graphs Amer Math Soc Colloqumm Pub Vol XXXVIII Amer Math Soc Providence Rhode Island 1962

Cited by 82 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Edge-vertex domination on interval graphs;Discrete Mathematics, Algorithms and Applications;2023-03-28

2. SaHNoC: an optimal energy efficient hybrid networks-on-chip architecture;The Journal of Supercomputing;2022-11-07

3. A linear-time algorithm for minimum k-hop dominating set of a cactus graph;Discrete Applied Mathematics;2022-10

4. Minimizing Congestion for Balanced Dominators;Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining;2022-08-14

5. Dominating Number on Icosahedral-Hexagonal Network;Mathematical Problems in Engineering;2021-04-10