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A note on the domination entropy of graphs | ||
| Journal of Discrete Mathematics and Its Applications | ||
| مقاله 2، دوره 10، شماره 1، خرداد 2025، صفحه 11-20 اصل مقاله (282.47 K) | ||
| نوع مقاله: Full Length Article | ||
| شناسه دیجیتال (DOI): 10.22061/jdma.2025.11448.1106 | ||
| نویسندگان | ||
| Arezoo N. Ghameshlou* 1؛ Amirhesam Jafari-Rad2؛ Mana Mohammadi2 | ||
| 1Department of Irrigation and Reclamation Engineering University of Tehran, P. O. Box 4111, Karaj, I. R. Iran | ||
| 2Department of Electrical Engineering, University of Tehran, Tehran, I. R. Iran | ||
| تاریخ دریافت: 21 آبان 1403، تاریخ بازنگری: 07 بهمن 1403، تاریخ پذیرش: 08 بهمن 1403 | ||
| چکیده | ||
| A dominating set of a graph G is a subset D of vertices such that every vertex outside D has a neighbor in D. The domination number of G, denoted by γ(G), is the minimum cardinality amongst all dominating sets of G. The domination entropy of G, denoted by Idom(G) is defined as Idom(G)=-∑i=1kdi(G)/γS(G)log (di(G)/γS(G)), where γS(G) is the number of all dominating sets of G and di(G) is the number of dominating sets of cardinality i. A graph G is C4-free if it does not contain a 4-cycle as a subgraph. In this note we first determine the domination entropy in the graphs whose complements are C4-free. We then propose an algorithm that computes the domination entropy in any given graph. We also consider circulant graphs G and determine di(G) under certain conditions on i. | ||
| کلیدواژهها | ||
| information؛ domination polynomial؛ domination entropy؛ algorithm؛ circulant graph | ||
| مراجع | ||
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