Upper bounds for covering total double Roman domination
Künye
Mojdeh, D. A. & Teymourzadeh, A. (2023). Upper bounds for covering total double Roman domination. TWMS Journal Of Applied And Engineering Mathematics, 13(3), 1029-1041.Özet
Let G = (V, E) be a finite simple graph where V = V (G) and E = E(G). Suppose that G has no isolated vertex. A covering total double Roman dominating function (CT DRD function) f of G is a total double Roman dominating function (T DRD function) of G for which the set {v ∈ V (G)|f(v) ≠ 0} is a covering set. The covering total double Roman domination number γctdR(G) is the minimum weight of a CT DRD function on G. In this work, we present some contributions to the study of γctdR(G)-function of graphs. For the non star trees T, we show that γctdR(T) ≤ 4n(T )+5s(T )−4l(T )/3, where n(T), s(T) and l(T) are the order, the number of support vertices and the number of leaves of T respectively. Moreover, we characterize trees T achieve this bound. Then we study the upper bound of the 2-edge connected graphs and show that, for a 2-edge connected graphs G, γctdR(G) ≤ 4n/3 and finally, we show that, for a simple graph G of order n with δ(G) ≥ 2, γctdR(G) ≤ 4n/3 and this bound is sharp.
Kaynak
TWMS Journal Of Applied And Engineering MathematicsCilt
13Sayı
3Bağlantı
https://hdl.handle.net/11729/5604http://jaem.isikun.edu.tr/web/index.php/archive/121-vol13no3/1090
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