[PDF] Top 20 Degree equitable line domination in graphs

... the domination number of G and is denoted by    G ...total domination number of G , denoted by  t   G is the minimum cardinality of total dominating set of G ... See full document

... the degree equitable domination number in ...between domination and degree equitable domination and independent ...the domination number, degree ... See full document

... the degree of the ...strong line set dominating number of G and is denote by ϑ sl ' ( G ) ...Strong Line set Dominating set are analyse with respect to the strong domination parameter for ... See full document

... The degree equitable domination has been studied in ...an equitable dominat- ing set of a graph if for every , there ex- ists a vertex such that uv and ... See full document

... be degree equitable connected co-total dominating set if for every vertex 𝑢𝑢 ∈ 𝑉𝑉 − 𝐷𝐷 there exist a vertex 𝑣𝑣 ∈ 𝐷𝐷 such that 𝑢𝑢𝑣𝑣 ∈ 𝐸𝐸(𝐺𝐺) and |𝑑𝑑𝑑𝑑𝑑𝑑(𝑢𝑢) − 𝑑𝑑𝑑𝑑𝑑𝑑(𝑣𝑣)| ≤ 1 provided < 𝑉𝑉 − 𝐷𝐷 > ... See full document

... There are many ways to represent the graph; one of the important graph representation is represent the graph by a polynomial. There are several well-studied graph polynomialslike chromatic polynomial, Tutte polynomial, ... See full document

... the degree of and degree of is less than or equal to 1, that is | ( ) − ( )| ≤ ...an equitable dominating set of is called the equitable domination number of and is denoted by ( ... See full document

... Let , ≥ 5 be a cycle with ( ) = { , , … , } and with E( ) = { , , … , }. Now obtain ( ) as follows: ( ) = ∪ , where = ( ) = { , , … , } and the set of newly added vertices = ; 1 ≤ ≤ . Note that the degree ... See full document

... the degree of any supporting vertices are at least three, that means in 𝐺 there are 𝑝 equitable isolated vertices and must be including in any dominating set of ... See full document

... We begin with simple, finite, undirected and connected graph G = (V (G), E(G)). For a vertex v ∈ V (G), the open neighborhood N(v) is defined as N(v) = {u ∈ V (G) : uv ∈ E(G)}. The maximum degree among the ... See full document

... the domination number (upper domination number) of G and is denoted by γ ( ) G , ( ( )) Γ G ...of domination is given in the book by Haynes etal [4] A survey of several advanced topics in ... See full document

... Roman domination is introduced by ...of domination and its parameters dependent, determine the graph that is the number of that parameter is ...all graphs with total domination number ... See full document

... Let 𝐷 = {𝑢 1 , 𝑣 1 } be a minimum total dominaing set of 𝐾 𝑛,𝑚 . Then, │𝑜𝑑 𝐷 (𝑢 1 ) − 𝑜𝑑 𝑉 2 −𝐷 (𝑣 𝑖 )│ ≤ 1 , for all 𝑣 𝑖 ∈ 𝑉 2 − 𝐷 and │𝑜𝑑 𝐷 (𝑣 1 ) − 𝑜𝑑 𝑉 1 −𝐷 (𝑢 𝑖 )│ ≤ 1 , for all 𝑢 𝑖 ∈ 𝑉 1 − 𝐷 . Hence, D is a near ... See full document

... of equitable domination in graphs, by considering the following real world problems like : in a network nodes with nearly equal capacity may interact with each other in a better way, in this society ... See full document

... A set S of vertices of G is called a detour dominating set if every vertex of G is detour dominated by some vertex in S. A detour dominating set of minimum cardinality is a minimum detour dominating set and its ... See full document

... Ali, Equitable coloring on Total graphs of Bigraphs and central graphs of cycles and paths, International Journal of Mathematics and Mathematical Sciences, Article ID 279246, 5 pages, ... See full document

... . Graphs have various special patterns like path, cycle, star, complete graph, bipartite graph complete graph, regular graph , strongly regular graph ...such graphs we refer to Harary ...the ... See full document

... Total domination in graphs was introduced by Cockayne, Dawes and Hedetniemi. A dominating set of a graph is a total dominating set, if its induced sub graph has no isolated vertices. Alternately we define a ... See full document

... multiple domination, which are called hr, si-domination and parametric ...classical domination are generalised for the hr, si-domina- tion and parametric domination ...vertex degree, ... See full document

... The aim of this article is to introduce a new definition of domination number in graphs called hn- domination number denoted by 𝛾 ℎ𝑛 (𝐺). This paper presents some properties which show the concepts ... See full document