For a graph G, a subset B of V (G) is called a boundary dominating set if every
vertex of V (G)B... more For a graph G, a subset B of V (G) is called a boundary dominating set if every vertex of V (G)B is vertex boundary dominated by some vertex of B. The boundary domination number b(G) of G is the minimum cardinality of minimum boundary dominating set in G. In this paper we computed Laplacian minimum boundary dominating energies of some standard graphs. Upper and lower bounds for LEB(G) are established.
In this paper we define the connected edge dominating set for a connected subgraph. We introduce ... more In this paper we define the connected edge dominating set for a connected subgraph. We introduce the connected boundary edge dominating set and analogous to the connected boundary edge domination number, we define the connected boundary edge domatic number in graphs. Exact values of some standard graphs are obtained and some other interesting results are established.
For a graph G, a subset B of V (G) is called a boundary dominating set if every vertex of V (G) ... more For a graph G, a subset B of V (G) is called a boundary dominating set if every vertex of V (G) S is vertex boundary dominated by some vertex of S. The boundary domination number b(G) of G is the minimum cardinality of minimum boundary dominating set in G. In this paper we introduce the minimum boundary dominating energy EB(G) of a graph G and computed minimum boundary dominating energies of some standard graphs. Upper and lower bounds for EB(G) are established.
In this paper we define the connected edge dominating set for a connected subgraph. We introduce ... more In this paper we define the connected edge dominating set for a connected subgraph. We introduce the connected boundary edge dominating set and analogous to the connected boundary edge domination number, we define the connected boundary edge domatic number in graphs. Exact values of some standard graphs are obtained and some other interesting results are established.
Let G = (V ;E) be a connected graph. A dominating set S V is called a connected dominating set ... more Let G = (V ;E) be a connected graph. A dominating set S V is called a connected dominating set if hSi is connected subgraph. In this paper we introduce the connected boundary dominating set and analogous to the connected boundary domination number, we de ne the connected boundary domatic number in graphs. Exact values of some standard graphs are obtained and some other interesting results are established.
Let G = (V;E) be a connected graph, A subset S of E(G) is
called a boundary edge dominating set i... more Let G = (V;E) be a connected graph, A subset S of E(G) is called a boundary edge dominating set if every edge of ES is edge boundary dominated by some edge of S. The minimum taken over all boundary edge dominating sets of a graph G is called the boundary edge domination number of G and is denoted by 0b(G). In this paper we introduce the edge boundary domination in graph. Exact values of some standard graphs are obtained and some other interesting results are established.
Let G = (V;E) be a connected graph. A subset S of V (G)
is called a boundary dominating set if ev... more Let G = (V;E) be a connected graph. A subset S of V (G) is called a boundary dominating set if every vertex of V S is boundary dominated by some vertex of S. The minimum taken over all boundary dominating sets of a graphGis called the boundary domination number of G and is denoted by b(G). We define the boundary domatic number in graphs. Exact values of of Wheel Graph Families are obtained and some other interesting results are established.
Let be a graph. A subset of is called a boundary dominating set of if every vertex in is vertex b... more Let be a graph. A subset of is called a boundary dominating set of if every vertex in is vertex boundary dominated by some vertex in . The minimum taken over all boundary dominating sets of is called the boundary domination number of and is denoted by . In this paper, we introduce the boundary domination and the boundary domatic number db (G) in Middle graph.
Let G = (V, E) be a connected graph, A subset S of V (G) is called a boundary dominating set if e... more Let G = (V, E) be a connected graph, A subset S of V (G) is called a boundary dominating set if every vertex of V (G) − S is vertex boundary dominated by some vertex of S. The minimum taken over all boundary dominating sets of G is called the boundary domination number of G and is denoted by γ b (G). In this paper we introduce the boundary domination in Total graph.
Let G be any graph. A dominating set D in G is called a paired dominating set if D contains a per... more Let G be any graph. A dominating set D in G is called a paired dominating set if D contains a perfect matching. The minimum cardinality of a paired-dominating set is called the paired-domination number, denoted by γ pd
An equitable dominating set D of a graph G = (V, E) is a split equitable dominating set if the in... more An equitable dominating set D of a graph G = (V, E) is a split equitable dominating set if the induced subgraph hV − Di is a disconnected. The split equitable domination number ϒse(G) of a graph G is the minimum cardinality of a split equitable dominating set. In this paper, we initiate the study of this new parameter and present some bounds and some exact values for ϒse(G). Also Nordhaus−Gaddum type results are obtained.
For a graph G, a subset B of V (G) is called a boundary dominating set if every
vertex of V (G)B... more For a graph G, a subset B of V (G) is called a boundary dominating set if every vertex of V (G)B is vertex boundary dominated by some vertex of B. The boundary domination number b(G) of G is the minimum cardinality of minimum boundary dominating set in G. In this paper we computed Laplacian minimum boundary dominating energies of some standard graphs. Upper and lower bounds for LEB(G) are established.
In this paper we define the connected edge dominating set for a connected subgraph. We introduce ... more In this paper we define the connected edge dominating set for a connected subgraph. We introduce the connected boundary edge dominating set and analogous to the connected boundary edge domination number, we define the connected boundary edge domatic number in graphs. Exact values of some standard graphs are obtained and some other interesting results are established.
For a graph G, a subset B of V (G) is called a boundary dominating set if every vertex of V (G) ... more For a graph G, a subset B of V (G) is called a boundary dominating set if every vertex of V (G) S is vertex boundary dominated by some vertex of S. The boundary domination number b(G) of G is the minimum cardinality of minimum boundary dominating set in G. In this paper we introduce the minimum boundary dominating energy EB(G) of a graph G and computed minimum boundary dominating energies of some standard graphs. Upper and lower bounds for EB(G) are established.
In this paper we define the connected edge dominating set for a connected subgraph. We introduce ... more In this paper we define the connected edge dominating set for a connected subgraph. We introduce the connected boundary edge dominating set and analogous to the connected boundary edge domination number, we define the connected boundary edge domatic number in graphs. Exact values of some standard graphs are obtained and some other interesting results are established.
Let G = (V ;E) be a connected graph. A dominating set S V is called a connected dominating set ... more Let G = (V ;E) be a connected graph. A dominating set S V is called a connected dominating set if hSi is connected subgraph. In this paper we introduce the connected boundary dominating set and analogous to the connected boundary domination number, we de ne the connected boundary domatic number in graphs. Exact values of some standard graphs are obtained and some other interesting results are established.
Let G = (V;E) be a connected graph, A subset S of E(G) is
called a boundary edge dominating set i... more Let G = (V;E) be a connected graph, A subset S of E(G) is called a boundary edge dominating set if every edge of ES is edge boundary dominated by some edge of S. The minimum taken over all boundary edge dominating sets of a graph G is called the boundary edge domination number of G and is denoted by 0b(G). In this paper we introduce the edge boundary domination in graph. Exact values of some standard graphs are obtained and some other interesting results are established.
Let G = (V;E) be a connected graph. A subset S of V (G)
is called a boundary dominating set if ev... more Let G = (V;E) be a connected graph. A subset S of V (G) is called a boundary dominating set if every vertex of V S is boundary dominated by some vertex of S. The minimum taken over all boundary dominating sets of a graphGis called the boundary domination number of G and is denoted by b(G). We define the boundary domatic number in graphs. Exact values of of Wheel Graph Families are obtained and some other interesting results are established.
Let be a graph. A subset of is called a boundary dominating set of if every vertex in is vertex b... more Let be a graph. A subset of is called a boundary dominating set of if every vertex in is vertex boundary dominated by some vertex in . The minimum taken over all boundary dominating sets of is called the boundary domination number of and is denoted by . In this paper, we introduce the boundary domination and the boundary domatic number db (G) in Middle graph.
Let G = (V, E) be a connected graph, A subset S of V (G) is called a boundary dominating set if e... more Let G = (V, E) be a connected graph, A subset S of V (G) is called a boundary dominating set if every vertex of V (G) − S is vertex boundary dominated by some vertex of S. The minimum taken over all boundary dominating sets of G is called the boundary domination number of G and is denoted by γ b (G). In this paper we introduce the boundary domination in Total graph.
Let G be any graph. A dominating set D in G is called a paired dominating set if D contains a per... more Let G be any graph. A dominating set D in G is called a paired dominating set if D contains a perfect matching. The minimum cardinality of a paired-dominating set is called the paired-domination number, denoted by γ pd
An equitable dominating set D of a graph G = (V, E) is a split equitable dominating set if the in... more An equitable dominating set D of a graph G = (V, E) is a split equitable dominating set if the induced subgraph hV − Di is a disconnected. The split equitable domination number ϒse(G) of a graph G is the minimum cardinality of a split equitable dominating set. In this paper, we initiate the study of this new parameter and present some bounds and some exact values for ϒse(G). Also Nordhaus−Gaddum type results are obtained.
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Papers by Dr. Puttaswamy
vertex of V (G)B is vertex boundary dominated by some vertex of B. The boundary
domination number
b(G) of G is the minimum cardinality of minimum boundary dominating
set in G. In this paper we computed Laplacian minimum boundary dominating
energies of some standard graphs. Upper and lower bounds for LEB(G) are established.
dominated by some vertex of S. The boundary domination number
b(G) of G is the minimum cardinality of minimum
boundary dominating set in G. In this paper we introduce the minimum boundary dominating energy EB(G) of a graph
G and computed minimum boundary dominating energies of some standard graphs. Upper and lower bounds for EB(G)
are established.
are obtained and some other interesting results are established.
called a boundary edge dominating set if every edge of ES is edge boundary dominated by some edge of S. The minimum taken over all boundary edge dominating sets of a graph G is called the boundary edge domination number of G and is denoted by 0b(G). In this paper we introduce the edge boundary domination in graph. Exact values of some standard graphs are obtained and some other interesting results are established.
is called a boundary dominating set if every vertex of V S is
boundary dominated by some vertex of S. The minimum taken
over all boundary dominating sets of a graphGis called the boundary
domination number of G and is denoted by b(G). We define the boundary domatic number in graphs. Exact values of of Wheel
Graph Families are obtained and some other interesting results are
established.
vertex of V (G)B is vertex boundary dominated by some vertex of B. The boundary
domination number
b(G) of G is the minimum cardinality of minimum boundary dominating
set in G. In this paper we computed Laplacian minimum boundary dominating
energies of some standard graphs. Upper and lower bounds for LEB(G) are established.
dominated by some vertex of S. The boundary domination number
b(G) of G is the minimum cardinality of minimum
boundary dominating set in G. In this paper we introduce the minimum boundary dominating energy EB(G) of a graph
G and computed minimum boundary dominating energies of some standard graphs. Upper and lower bounds for EB(G)
are established.
are obtained and some other interesting results are established.
called a boundary edge dominating set if every edge of ES is edge boundary dominated by some edge of S. The minimum taken over all boundary edge dominating sets of a graph G is called the boundary edge domination number of G and is denoted by 0b(G). In this paper we introduce the edge boundary domination in graph. Exact values of some standard graphs are obtained and some other interesting results are established.
is called a boundary dominating set if every vertex of V S is
boundary dominated by some vertex of S. The minimum taken
over all boundary dominating sets of a graphGis called the boundary
domination number of G and is denoted by b(G). We define the boundary domatic number in graphs. Exact values of of Wheel
Graph Families are obtained and some other interesting results are
established.