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Strong line domination in graphs

Author:

M. H. Muddebihal and Nawazoddin U. Patel

Subject Area:

Physical Sciences and Engineering

Abstract:

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 the set of edges of G in which two vertices are adjacent if and only if the corresponding edges of G are adjacent. A dominating set D of a graph L(G) is a strong Line dominating set if every vertex in 〈V[L(G) ]-D〉 is strongly dominated by at least one vertex in D. Strong Line domination number 〖 γ〗_(SL ) (G) of G is the minimum cardinality of strong Line dominating set of G. In this paper, we study graph theoretic properties of 〖 γ〗_(SL ) (G) and many bounds were obtain in terms of elements of G and its relationship with other domination parameters were found.

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