Open AccessTotal and Inverse Domination Numbers of Certain Graphs
Author(s) -
V. Shalini,
Indra Rajasingh
Publication year - 2021
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/1012/1/012066
Subject(s) - dominating set , combinatorics , vertex (graph theory) , domination analysis , mathematics , inverse , graph , cardinality (data modeling) , connectivity , discrete mathematics , computer science , geometry , data mining
For any graph G having vertex set V ( G ) then the subset set D ⊆ V ( G ) is known as a dominating set if every single vertex of G not belonging to D is adjoining to not less than one vertex in D . The domination number γ ( G ) is the minimum number of elements contained in a minimum dominating set D of G . Any subset D in V ( G ) is known as total domianting set if each and every vertex of V in G is adjoining to not less than one vertex of D . The set which contains minimum number of elements among all total dominating set is the minimum total dominating set and its cardinality denoted as total domination number γ t ( G ). The inverse dominating set D ′ is defined as that D is a minimum dominating set of G , if there exist an another dominating set say D ′ in V − D corresponding to D and its cardinality is the inverse domination number γ ′ ( G ). In this paper we give the total and inverse domination numbers of certain graphs.