Submit your paper : editorIJETjournal@gmail.com
Paper Title : SET-DOMINATION IN LINE GRAPHS
ISSN : 2395-1303
Year of Publication : 2022
MLA Style: -Sana Aejaz, M.H.Muddebihal, D.G.Akka , SET-DOMINATION IN LINE GRAPHS " " Volume 8 - Issue 1 January - February,2022 International Journal of Engineering and Techniques (IJET) ,ISSN:2395-1303 , www.ijetjournal.org
APA Style: - Sana Aejaz, M.H.Muddebihal, D.G.Akka " SET-DOMINATION IN LINE GRAPHS " Volume 8 - Issue 1 January - February,2022 International Journal of Engineering and Techniques (IJET) ,ISSN:2395-1303 , www.ijetjournal.org
In this paper, we initiate the study of set-domination in line graph 𝐿(𝐺) of a graph 𝐺.The line graph 𝐿(𝐺) of a graph 𝐺 is the graph whose vertex set is in one-to-one correspondence with the elements of the set 𝐸 such that two vertices of 𝐿(𝐺) are adjacent if and only if they correspond to two adjacent edge of 𝐺.In this paper, many bounds of 𝛾𝑠𝑑[𝐿(𝐺)] were obtained.Also its exact values for some standard graphs were found.
. R.B.Allan and R.Laskar, On domination and independent domination number of a graph, Discrete Mathematics, Vol-23, 1978, 73-76. . E.J.Cockayne, R.M.Dawes and S.T.Hedetniemi, Total domination in graphs, Networks, Vol-10, 1980, 211-219. . E.J.Cocakyne, B.L.Hartnell, S.T.Hedetniemi and R.Laskar, Perfect domination in graphs, Journal of Combinatorics,Information & System sciences, Vol-18(1993),136-148. . F.Harary, Graph theory, Adisonwesley, Reading mass, 1974. . T.W.Haynes, S.T.Hedetniemi and P.J.Slater, Domination in graphs: Advanced topics (Marcel Decker, New York, 1998). . T.Haynes, S.T.Hedetniemi and P.J.Slater, Fundamentals of domination in graphs (Marcel Decker, New York,1998). . S.T.Hedetniemi and R.C.Laskar, Connected domination in graphs, Graph theory and Combinatorics, Cambridge (Academic press), London 1948, 209-218. . Jayaram, S.R(1997), Line domination in graphs, Graph Combinatorics 357-363. . V.R.Kulli, Theory of domination in graphs, Viswa international publications, India-2010 . S.Mitchell, S.T.Hedetniemi, Edge domination in trees, Congressus Numerantium 19(1977)489-509. . M.H.Muddebihal and Geetadevi Baburao, “Weak line domination in graph theory” IJRAR, Vol-6, 2019, 129-133. . E.Sampath Kumar, L.Pushpa Latha, “Set-domination in graphs”, Aug-1994, Journal of graph theory/Vol-18, Issue-5.
-Line Graph, Set-domination, cototal domination, perfect domination, total domination.
Mathematics Subject Classification: AMS-05C69, 05C70, 05C76.