A note on the total domination supercritical graphs
عنوان مقاله: A note on the total domination supercritical graphs
شناسه ملی مقاله: JR_COMB-1-3_001
منتشر شده در در سال 1391
شناسه ملی مقاله: JR_COMB-1-3_001
منتشر شده در در سال 1391
مشخصات نویسندگان مقاله:
Abdollah Alimadadi - Shahid Beheshti University
Changiz Eslahchi - Shahid Beheshti University
Nader Jafari Rad - Shahrood University of Technology
خلاصه مقاله:
Abdollah Alimadadi - Shahid Beheshti University
Changiz Eslahchi - Shahid Beheshti University
Nader Jafari Rad - Shahrood University of Technology
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-۲ for all e\in E(H). The ۲۰۰۲ 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, ۲۵۸ (۲۰۰۲), ۳۶۱-۳۷۱, presents a theorem (Theorem ۱۱) to produce (۲k + ۲)-supercritical graphs relative to K_{۲k+۱, ۲k+۱} of diameter ۵, for each k\geq ۲. However, the families of graphs in their proof are not the case. We present a correction of this theorem.
کلمات کلیدی: Total domination, Supercritical, Diameter
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1319386/