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Alimadadi, Abdollah, Eslahchi, Changiz, Jafari Rad, Nader. (1391). A note on the total domination supercritical graphs. , 1(3), 1-4. doi: 10.22108/toc.2012.1829
Abdollah Alimadadi; Changiz Eslahchi; Nader Jafari Rad. "A note on the total domination supercritical graphs". , 1, 3, 1391, 1-4. doi: 10.22108/toc.2012.1829
Alimadadi, Abdollah, Eslahchi, Changiz, Jafari Rad, Nader. (1391). 'A note on the total domination supercritical graphs', , 1(3), pp. 1-4. doi: 10.22108/toc.2012.1829
Alimadadi, Abdollah, Eslahchi, Changiz, Jafari Rad, Nader. A note on the total domination supercritical graphs. , 1391; 1(3): 1-4. doi: 10.22108/toc.2012.1829

A note on the total domination supercritical graphs

Transactions on Combinatorics
مقاله 1، دوره 1، شماره 3، آذر 2012، صفحه 1-4    اصل مقاله (400.61 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2012.1829
نویسندگان
Abdollah Alimadadi1؛ Changiz Eslahchi1؛ Nader Jafari Rad* 2
1Shahid Beheshti University
2Shahrood University of Technology
چکیده
‎Let $G$ be a connected spanning subgraph of $K_{s,s}$ and let $H$‎ ‎be the complement of $G$ relative to $K_{s,s}$‎. ‎The graph $G$ is‎ ‎$k$-supercritical relative to $K_{s,s}$ if $\gamma_t(G)=k$‎ ‎and $\gamma_t(G+e)=k-2$ for all $e\in E(H)$‎. ‎The 2002 paper by‎ ‎T.W‎. ‎Haynes‎, ‎M. A‎. ‎Henning and L.C‎. ‎van der Merwe‎, ‎``Total‎ ‎domination supercritical graphs with respect to relative‎ ‎complements‎" ‎that appeared in Discrete Mathematics‎, ‎258 (2002)‎, ‎361-371‎, ‎presents a theorem (Theorem 11) to produce $(2k‎ + ‎2)$-supercritical graphs relative to $K_{2k+1‎, ‎2k+1}$ of diameter‎ ‎$5$‎, ‎for each $k\geq 2$‎. ‎However‎, ‎the families of graphs in their‎ ‎proof are not the case‎. ‎We present a correction of this theorem‎.
کلیدواژه‌ها
Total domination؛ Supercritical؛ Diameter
مراجع
A. Alimadadi, Ch. Eslahchi, T. W. Haynes, M. A. Henning, N. Jafari Rad and L. C. van der Merwe (2012) Erratum to "Total domination supercritical graphs with respect to relative complements [Discrete Math., {bf 258} (2002) 361-371], Discrete Math 312, 1076
T. W. Haynes, S. T. Hedetniemi and P. J. Slater (1998) Fundamentals of Domination in Graphs Marcel Dekker, NewYork
T. W. Haynes, M. A. Henning, and L. C. van der Merwe (2002) Total domination supercritical graphs with respect to relative complements Total domination supercritical graphs with respect to relative complements 258, 361-371
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