A Nordhaus-Gaddum inequality on the total double Roman domination number of graphs
The total double Roman domination number of the graph has important applications in circuit diagram design,computer programming and bioengineering structure,and therefore it is of theoretical value to explore the upper and lower bounds of the total double Roman domination number.This paper discusses the relationship between the upper bound of the total double Roman domination number of graphs and complements and its minimum vertex degree,and finds the minimum vertex subset required to construct the total double Roman domination by constructing the maximum vertex subset in reverse,and combines the disproof method to study,we conclude that there is an association between the total double Roman domination of graph G and its complement and the minimum vertex degree of the graph and its complement when both the graph G and its complement graph have a diameter of 2,and some results are given about the Nordhaus-Gaddum inequality of the total double Roman control of the graph.The research results and research methods provide a theoretical basis for calculating the upper bound of the total double Roman control numbers of the connected graph,popularize the research results of Jager,and help to design the optimization algorithm for finding the total double Roman control numbers on the interval graph,which has application value in military planning,engineering,medicine,etc.
Nordhaus-Gaddum inequalitytotal double Roman dominationtotal double Roman domination numbercomplement graph
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