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标题：D- Complement and D(i)- Complement of a Graph
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作者：Sabitha D'Souza ; Shankar Upadhyay ; Swati Nayak 等
期刊名称：Lecture Notes in Engineering and Computer Science
印刷版ISSN：2078-0958
电子版ISSN：2078-0966
出版年度：2022
卷号：52
期号：1
语种：English
出版社：Newswood and International Association of Engineers
摘要：A dominating set for a graph G = (V, E) is asubset D of V such that every point not in D is adjacent to atleast one member of D. Let P = {V1, V2, . . . , Vk} be a partitionof point set V (G). For all Vi and Vj in P of order k ≥ 2, i ̸= j,delete the lines between Vi and Vj in G and include the linesbetween Vi and Vj which are not in G. The resultant graph thusobtained is k−complement of G with respect to the partition Pand is denoted by GkP . For each set Vr in P of order k ≥ 1,delete the lines of G inside Vr and insert the lines of G joiningthe points of Vr. The graph GkP(i)thus obtained is called thek(i)−complement of G with respect to the partition P. In thispaper, we define D−complement and D(i)−complement of agraph G. Further we study various properties of D and D(i)complements of a given graph.
关键词：D−complement; D(i)−complement;γ−complement and γ(i)−complement.