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On mixed double Roman domination number and 2-independence number of graphs | ||
| Journal of Discrete Mathematics and Its Applications | ||
| دوره 11، شماره 3، آذر 2026، صفحه 163-175 اصل مقاله (376.61 K) | ||
| نوع مقاله: Full Length Article | ||
| شناسه دیجیتال (DOI): 10.22061/jdma.2026.12594.1170 | ||
| نویسندگان | ||
| Halimeh Koulivand1؛ Mohammad Habibi* 2؛ Hassan Arianpoor1؛ Mina Valinavaz3 | ||
| 1Department of Mathematics, Tafresh University, Tafresh, Iran. | ||
| 2Tafresh University | ||
| 3Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran. | ||
| تاریخ دریافت: 13 مهر 1404، تاریخ بازنگری: 02 بهمن 1404، تاریخ پذیرش: 07 بهمن 1404 | ||
| چکیده | ||
| Let G=(V(G),E(G)) be a simple graph. A mixed double Roman dominating function (MDRDF) on G is a function f:V(G)∪E(G) → {0,1,2,3} such that (i) if f(u)=0, then u has at least two neighbors assigned 2 under f or one neighbor w with f(w)=3; (ii) if f(u)=1, then u must have at least one neighbor w with f(w)≥ 2. The weight of f is equal to Σu∈V(G)∪E(G)f(u). The mixed double Roman domination number γdR*(G) is the minimum weight among all MDRDF's of G. A subset X of V(G) is a 2-independent set of G if the subgraph induced by the vertices of X is isomorphic to rK2∪sK1, where 2r+s=|X|. The maximum cardinality of a 2-independent set of G is the 2-independence number β2(G). In this paper, it is shown that these parameters are incomparable, in general. Also, we prove that either T is a path or a tree with a quasi-diagonal path u1,…, uk such that d(u2)≠ 2 or d(u3)≠ 2, then γdR*(T)≤ 2β2(T). Moreover, all extremal trees in this family that attaining equality are characterized. | ||
| کلیدواژهها | ||
| 2-independence number؛ mixed double Roman domination number؛ tree | ||
| مراجع | ||
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