JISE


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Journal of Information Science and Engineering, Vol. 40 No. 2, pp. 253-264


Determining the 2-Tuple Total Domination Number of a Harary Graph under Specific Degree Conditions

MIN-SHU JAO1, HUNG-LUNG WANG1,+, JOU-MING CHANG2
AND CHIA-WEN WU2
1Department of Computer Science and Information Engineering
National Taiwan Normal University
Taipei City, 116 Taiwan
E-mail: {40747033s; hlwang}@ntnu.edu.tw
2Institute of Information and Decision Sciences
National Taipei University of Business
Taipei City, 100 Taiwan
E-mail: spade@ntub.edu.tw

Given a graph G, a 2-tuple total dominating set is a vertex subset S such that every vertex has at least two neighbors in S. The cardinality of a minimum 2-tuple total dominating set is called the 2-tuple total domination number. In this paper, we determine the 2-tuple total domination numbers of Hm,n for m ∈ {3,5}, where Hm,n stands for a Harary graph of n vertices with degree parameter m.

Keywords: graph theory, domination, 2-tuple total domination, regular graphs, Harary graphs

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