2018/10/20 by Farshad Kazemnejad, Kazemnejad, Farshad, Adel P. Kazemi +3
Computer Science · #05C69 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1810.08773
openalex publication_date 2018/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a graph G=(V,E), we call a subset S⊆ V ∪ E a total mixed dominating set of G if each element of V ∪ E is either adjacent or incident to an element of S, and the total mixed domination number γtm(G) of G is the minimum cardinality of a total mixed dominating set of G. In this paper, we initiate to study the total mixed domination number of a connected graph by giving some tight bounds in terms of some parameters such as order and total domination numbers of the graph and its line graph. Then we discuss on the relation between total mixed domination number of a graph and its diameter. Studing of this number in trees is our next work. Also we show that the total mixed domination number of a graph is equale to the total domination number of a graph which is obtained by the graph. Giving the total mixed domination numbers of some special graphs is our last work.