Jayaram Ramaswamy | Jain University (original) (raw)
Born in 1952 educated in Mysore University and earned a doctrate degree in Mathematics from Karnatak University Dharwar.
Taugght athematics i schools including the Rishivaley school, The Hyderbad Public school ad college including JNNCE, Shimoga, PESIT Bangalore and SBMJCE, Bangalore
Supervisors: E Sampathkumarachar, University of Mysore
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Papers by Jayaram Ramaswamy
Preprint, 2013
In this paper we introduce the concept of Energy of a Graph based on the minimum neighbourhood se... more In this paper we introduce the concept of Energy of a Graph based on the minimum neighbourhood set of the graph. This energy is computed for some class of graphs.
Nbd sets, 2017
A subset S of a vertex set V(G) such that a vertex in V(G)-S is adjacent to a vertex in S is a do... more A subset S of a vertex set V(G) such that a vertex in V(G)-S is adjacent to a vertex in S is a dominating set of G. The minimum cardinality among all dominating sets of the graph is the domination number. A subset S of the vertex set is a neighbourhood set if the graph is the union of the sub graphs induced by the closed neighbourhoods of the vertices of the subset S. The minimum cardinality among all minimal neighbourhood sets is the neighbourhood number of the graph. The notion of a dominating set of a graph was introduced by Oystein Ore in 1962. This concept is generalized to the Neighbourhood set by Sampathkumar and Neeralagi in 1985. In this paper we trace the development of the above concepts and results. We list open problems and conjectures on neighbourhood number and neighbourhood sets in graphs.
A subset S of a vertex set V(G) such that a vertex in V(G) -S is adjacent to a vertex in S is a d... more A subset S of a vertex set V(G) such that a vertex in V(G) -S is adjacent to a vertex in S is a dominating set of G. The minimum cardinality among all dominating sets of the graph is the domination number. A subset S of the vertex set is a neighbourhood set if the graph is the union of the sub graphs induced by the closed neighbourhoods of the vertices of the subset S. The minimum cardinality among all minimal neighbourhood sets is the neighbourhood number of the graph. The notion of a dominating set of a graph was introduced by Oystein Ore in 1962. This concept is generalized to the Neighbourhood set by Sampathkumar and Neeralagi in 1985.
Preprint, 2013
In this paper we introduce the concept of Energy of a Graph based on the minimum neighbourhood se... more In this paper we introduce the concept of Energy of a Graph based on the minimum neighbourhood set of the graph. This energy is computed for some class of graphs.
Nbd sets, 2017
A subset S of a vertex set V(G) such that a vertex in V(G)-S is adjacent to a vertex in S is a do... more A subset S of a vertex set V(G) such that a vertex in V(G)-S is adjacent to a vertex in S is a dominating set of G. The minimum cardinality among all dominating sets of the graph is the domination number. A subset S of the vertex set is a neighbourhood set if the graph is the union of the sub graphs induced by the closed neighbourhoods of the vertices of the subset S. The minimum cardinality among all minimal neighbourhood sets is the neighbourhood number of the graph. The notion of a dominating set of a graph was introduced by Oystein Ore in 1962. This concept is generalized to the Neighbourhood set by Sampathkumar and Neeralagi in 1985. In this paper we trace the development of the above concepts and results. We list open problems and conjectures on neighbourhood number and neighbourhood sets in graphs.
A subset S of a vertex set V(G) such that a vertex in V(G) -S is adjacent to a vertex in S is a d... more A subset S of a vertex set V(G) such that a vertex in V(G) -S is adjacent to a vertex in S is a dominating set of G. The minimum cardinality among all dominating sets of the graph is the domination number. A subset S of the vertex set is a neighbourhood set if the graph is the union of the sub graphs induced by the closed neighbourhoods of the vertices of the subset S. The minimum cardinality among all minimal neighbourhood sets is the neighbourhood number of the graph. The notion of a dominating set of a graph was introduced by Oystein Ore in 1962. This concept is generalized to the Neighbourhood set by Sampathkumar and Neeralagi in 1985.