Results on Coregular Perfect Domination of Line Graph and Relation with Different Dominations of Graph

Full Text (PDF, 381KB), PP.45-50

Views: 0 Downloads: 0


M. H Muddebihal 1 N. Jayasudha 2,*

1. Department of Mathematics, Gulbarga University, Kalaburagi- 585106, India

2. Department of Mathematics, Sharnbasva University, Kalaburagi- 585103, India

* Corresponding author.


Received: 31 May 2022 / Revised: 29 Jun. 2022 / Accepted: 16 Aug. 2022 / Published: 8 Feb. 2023

Index Terms

Graph, Line graph, Co- regular perfect dominating set, Co-regular perfect domination number


For any graph G = (V, E),the line graph L(G)of a graph G is a graph whose set of vertices is the union of set of edges of G in which two vertices of L(G) are adjacent if and only if the corresponding edges of G are adjacent. A dominating set D_1 ⊆ V[L(G)] is called coregular perfect dominating set, if the induced subgraph < V[L(G)]-D_1 > is regular. The minimum cardinality of vertices in such a set is called coregular perfect domination number in L(G) and is represented by γ_cop [L(G)].
In this Article, we study the graph theoretic properties of γ_cop [L(G)] and many bounds were obtained in terms of elements of G and its relationship with other domination parameters were found .Our investigation on this work is to establish the application oriented standard results in the field of domination theory for several kinds of new concepts which are playing an important role of application.

Cite This Paper

M. H Muddebihal, N. Jayasudha, "Results on Coregular Perfect Domination of Line Graph and Relation with Different Dominations of Graph", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.9, No.1, pp. 45-50, 2023. DOI: 10.5815/ijmsc.2023.01.05


[1]R.B Allan and R.Laskar,on domination and independent domination number of a graph, Discrete Mathematics Vol – 23 (1978) , 73 - 76.
[2]S.Arumugam and S.Velammal, 1998.Edge domination in graphs, Taiwanese J.of Mathematics, 2(2),173-179.
[3]L.W. Beineke and R.J.Wilson , Selected topics in Graph theory. Academic press, London (1978)
[4]C.Berge, 1962. Theory of graphs and its applications, Methuen, London.
[5]E.J Cockayne, R.M dawer and S.T Hedetneimi ,Total domination in graphs, Networks, 10 (1980) , 211- 219.
[6]M.R Fellows and M.N Hoover , Perfect domination , Australia , J.Combinatorics , 3(1999), 141-150.
[7]F.Harary , Graph theory , Adison wisely Reading Mass (1972).
[8]S.T.Hededetniemi and R.C.Laskar,Connected domination in graphs.Graph Theory and Combinatorics.(Cambridge.1983) Academic press, London (1984) 209-217
[9]V.R Kulli , Theory of domination in graphs , Viswa international publications (2010).
[10]V.R Kulli. The cototal domination number of a graph , J.disc Math, sci and cryptography, 2(1999), 179-184
[11]M. Livingston and Q. F. Stout, Perfect dominating sets Congr Number,79; (1990),187-203.
[12]S..L Mitchell and S.T Hedetneimi ,Edge domination in trees , Congr. Numer.19 (1977) ,489-509.
[13]M.H.Muddebihal, Abdual Gaffar and Shabbir Ahmed, Regular number of line graph. International journal of Applied Research vol (10) (sept 2015) 937-939.
[14]M.H.Muddebihal , U.A.Panfarosh and Anil R.Sedamkar, Regular total domination in line graphs , International Journal of Science and Technology , vol.3, No.3, April-2014, pp. 119-126
[15]E.Sampath Kumar and H.B Walikar ,The connected domination number of graph , J.Math Phy sci , 13 (1979) , 607- 613.