Secure Sets and Defensive Alliances in Graphs: A Faster Algorithm and Improved Bounds

Author:

AMANO Kazuyuki1,OO Kyaw May2,OTACHI Yota3,UEHARA Ryuhei3

Affiliation:

1. Depertment of Computer Science, Gunma University

2. University of Computer Studies, Yangon

3. School of Information Science, Japan Advanced Institute of Science and Technology

Publisher

Institute of Electronics, Information and Communications Engineers (IEICE)

Subject

Artificial Intelligence,Electrical and Electronic Engineering,Computer Vision and Pattern Recognition,Hardware and Architecture,Software

Reference17 articles.

1. [1] R.C. Brigham, R.D. Dutton, and S.T. Hedetniemi, “Security in graphs,” Discrete Appl. Math., vol.155, pp.1708-1714, 2007.

2. [2] F.R.K. Chung, Z. Füredi, R.L. Graham, and P.D. Seymour, “On induced subgraphs of the cube,” J. Comb. Theory, Ser. A, vol.49, pp.180-187, 1988.

3. [3] R.D. Dutton, “The evolution of a hard graph theory problem — secure sets,” A course material of COT 6410: Computational Complexity, University of Central Florida, 2010. Available at http://www.cs.ucf.edu/courses/cot6410/spr2010/doc/SecureSets.doc

4. [4] R.D. Dutton, “On a graph's security number,” Discrete Math., vol.309, pp.4443-4447, 2009.

5. [5] R.D. Dutton, R. Lee, and R.C. Brigham, “Bounds on a graph's security number,” Discrete Appl. Math., vol.156, pp.695-704, 2008.

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1. On the security number of the Cartesian product of graphs;Discrete Applied Mathematics;2021-12

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