On the inverse signed total domination number in graphs

• Autorzy: Mojdeh D. A. , Samadi B.

Identyfikatory

DOI

10.7494/OpMath.2017.37.3.447

• Języki publikacji: EN

Abstrakty

EN

In this paper, we study the inverse signed total domination number in graphs and present new sharp lower and upper bounds on this parameter. For example by making use of the classic theorem of Turán (1941), we present a sharp upper bound on Kr+1-free graphs for r ≥ 2. Also, we bound this parameter for a tree from below in terms of its order and the number of leaves and characterize all trees attaining this bound.

Słowa kluczowe

EN

inverse signed total dominating function; inverse signed total domination number; k-tuple total domination number

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2017
• Tom: Vol. 37, no. 3
• Strony: 447--456
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Mojdeh D. A.

• University of Mazandaran Department of Mathematics Babolsar, Iran

autor

Samadi B.

• University of Mazandaran Department of Mathematics Babolsar, Iran

Bibliografia

• [1] M. Atapour, S. Norouzian, S.M. Sheikholeslami, L. Volkmann, Bounds on the inverse signed total domination numbers in graphs, Opuscula Math. 36 (2016) 2, 145–152.
• [2] M.A. Henning, Signed total domination in graphs, Discrete Math. 278 (2004), 109–125.
• [3] S.M. Hosseini Moghaddam, D.A. Mojdeh, B. Samadi, L. Volkmann, New bounds on the signed total domination number of graphs, Discuss. Math. Graph Theory 36 (2016), 467–477.
• [4] Z. Huang, Z. Feng, H. Xing, Inverse signed total domination numbers of some kinds of graphs, Information Computing and Applications Communications in Computer and Information Science ICICA 2012, Part II, CCIS 308 (2012), 315–321.
• [5] V. Kulli, On n-total domination number in graphs, Graph Theory, Combinatorics, Algorithms and Applications, SIAM, Philadelphia, 1991, 319–324.
• [6] D.A. Mojdeh, A. Sayed Khalkhali, H. Abdollahzadeh, Y. Zhao, Total k-distance domination critical graphs, Transaction on Combinatorics 5 (2016) 3, 1–9.
• [7] P. Turán, On an extremal problem in graph theory, Math. Fiz. Lapok 48 (1941), 436–452.
• [8] C. Wang, The negative decision number in graphs, Australas. J. Combin. 41 (2008), 263–272.
• [9] C. Wang, Lower negative decision number in a graph, J. Appl. Math. Comput. 34 (2010), 373–384.
• [10] H. Wang, E. Shan, Signed total 2-independence in graphs, Utilitas Math. 74 (2007), 199–206.
• [11] D.B. West, Introduction to Graph Theory, 2nd ed., Prentice Hall, 2001.
• [12] B. Zelinka, Signed total domination number of a graph, Czechoslovak Math. J. 51 (2001), 225–229.

Uwagi

EN

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).