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A note on independent domination in almost-regular graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 29 فروردین 1405 اصل مقاله (332.23 K) | ||
| نوع مقاله: Special issue of CCO to honor Odile Favaron | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.31146.2756 | ||
| نویسندگان | ||
| Wayne Goddard* 1، 2؛ Michael A. Henning2 | ||
| 1School of Mathematical and Statistical Sciences, Clemson University, Clemson, USA | ||
| 2Department of Mathematics and Applied Mathematics, University of Johannesburg Auckland Park, 2006 South Africa | ||
| چکیده | ||
| A classic result in domination theory is that a regular graph has independent domination number at most half the order. We strengthen this result to ``almost-regular'' graphs by showing that if a graph has minimum degree $\delta > 0$ and maximum degree at most $\delta + 3$, and the subgraph induced by the vertices of degree $\delta + 3$ (if any) is bipartite, then the independent domination number is at most half the order. We also discuss related questions. | ||
| کلیدواژهها | ||
| Independent domination؛ Almost-regular graph؛ one-half bound | ||
| مراجع | ||
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[8] W. Goddard, M.A. Henning, J. Lyle, and J. Southey, On the independent domination number of regular graphs, Annals Combin. 16 (2012), 719–732. https://doi.org/10.1007/s00026-012-0155-4
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