On some results of perfect dominations of some graphs
Künye
Caay, M. L. & Palahang Jr., S. R. (2022). On some results of perfect dominations of some graphs. TWMS Journal Of Applied And Engineering Mathematics, 12(2), 600-607.Özet
A dominating set D ⊆ V (G) of a simple graph G is the set of all u such that for every v ∈ V (G)\D, uv ∈ E(G). An independent set I ⊆ V (G) is a set of non-adjacent vertices in G. An independent dominating set Di ⊆ V (G) is a subset of V (G) that is both independent set and dominating set. A subset S of V (G) is called a perfect dominating set of S if for each v belongs to V (G)\S, there exists a unique element u ∈ S, such that v and u are adjacent. Define an independent perfect dominating set Dip of G to be a dominating set that is both independent dominating set and perfect dominating set. The minimum cardinality of an independent perfect dominating set of G is called an independent perfect domination number of G, denoted by γip(G). If a graph has a perfect dominating set, we say that the graph G is γip-graph. In this study, we determine some bounds and parameters of the graph as well as the existence existence of this invariant to some graphs and graphs formed by some binary operations.
Kaynak
TWMS Journal Of Applied And Engineering MathematicsCilt
12Sayı
2Bağlantı
https://hdl.handle.net/11729/3840http://jaem.isikun.edu.tr/web/index.php/archive/115-vol12no2/845
Koleksiyonlar
Aşağıdaki lisans dosyası bu öğe ile ilişkilidir:
İlgili Öğeler
Başlık, yazar, küratör ve konuya göre gösterilen ilgili öğeler.
-
Total roman domination number of graphs
Thakkar, Dineshbhai; Badiyani, Sanket (Işık University Press, 2022)In this paper a characterization of minimal total roman dominating functions has been proved. It has also been proved that if v is a pendant vertex and its neighbor u is not a pendant vertex then f(v) = 0 or 1 for any ... -
Secure point set domination in graphs
Gupta, Purnima; Goyal, Alka (Işık University Press, 2024-04)In this paper, we introduce the notion of secure point-set domination in graphs. A point-set dominating D of graph G is called a secure point-set dominating set if for every vertex u ∈ V −D, there exists a vertex v ∈ D∩N(u) ... -
Graphs with equal domination and independent domination number
Vaidya, Samir K.; Pandit, R. M. (Işık University Press, 2015)A set S of vertices of a graph G is an independent dominating set of G if S is an independent set and every vertex not in S is adjacent to a vertex in S. The independent domination number of G, denoted by i(G), is the ...