Papers by Meenal Nachiappan
Let G(V, E) be a simple, finite and undirected connected graph. A non-empty set S ⊆ V of a graph ... more Let G(V, E) be a simple, finite and undirected connected graph. A non-empty set S ⊆ V of a graph G is a dominating set, if every vertex in V − S is adjacent to atleast one vertex in S. A dominating set S ⊆ V is called a locating dominating set, if for any two vertices v, w ∈ V − S, N (v) ∩ S = N (w) ∩ S. A locating dominating set S ⊆ V is called a co-isolated locating dominating set (cild-set), if there exists atleast one isolated vertex in V − S. The co-isolated locating domination number γ cild is the minimum cardinality of a co-isolated locating dominating set. In this paper, some bounds on co-isolated locating domination number are obtained. Also minimal cild-sets are characterized. Further the graphs for which γ cild to be p − 2 are obtained.
Let G (V, E) be a simple, finite and undirected connected graph. A nonempty set S V of a graph G ... more Let G (V, E) be a simple, finite and undirected connected graph. A nonempty set S V of a graph G is a dominating set, if every vertex in V -S is adjacent to atleast one vertex in S. A dominating set S V is called a locating dominating set, if for any two vertices v, w V -S, N(v) S N(w) S. A locating dominating set S V is called a coisolated locating dominating set (cildset), if there exists atleast one isolated vertex in <V -S >. The domination number (G) of a graph G is the minimum cardinality of a dominating set. The locating domination number ld (G) and coisolated locating domination number cild (G) are defined in the same way. A partition of V(G), all of whose classes are cildsets in G is called a coisolated locating domatic partition of G. The maximum number of classes of a coisolated locating domatic partition of G is called the coisolated locating domatic number of G and denoted by d cild (G). In this paper, connected graphs satisfying the relation cild (G) ld (G) (G) are constructed. Also the bounds for d cild (G) are obtained.
be a simple, finite, undirected connected graph. A dominating set S V is called a locating domi... more be a simple, finite, undirected connected graph. A dominating set S V is called a locating dominating set, if for any two vertices v, w V -S, N(v) S N(w) S. A locating dominating set S V is called a coisolated locating dominating set, if there exists atleast one isolated vertex in <V -S >. Dcild is the number of minimum coisolated locating dominating set of a graph G. The coisolated locating domination number cild is the minimum cardinality of a coisolated locating dominating set. In this paper average coisolated domination number agcild (G) is defined and, cild and agcild are obtained for binomial trees, binary trees, ternary trees and complete cary trees. Also the bounds for agcild (G) are found.
Let G (V, E) be a simple, finite, undirected connected graph. A non – empty set S V of a graph ... more Let G (V, E) be a simple, finite, undirected connected graph. A non – empty set S V of a graph G is a dominating set, if every vertex in V – S is adjacent to atleast one vertex in S. A dominating set S V is called a locating dominating set, if for any two vertices v, w V – S, N(v) S N(w) S. A locating dominating set S V is called a co – isolated locating dominating set, if there exists atleast one isolated vertex in <V – S >. The co – isolated locating domination number cild is the minimum cardinality of a co – isolated locating dominating set. In this paper, the number cild is obtained for unicyclic graphs.
Let G(V, E) be a simple, finite, undirected connected graph. A non-empty set S ⊆ V of a graph G i... more Let G(V, E) be a simple, finite, undirected connected graph. A non-empty set S ⊆ V of a graph G is a dominating set, if every vertex in V − S is adjacent to atleast one vertex in S. A dominating set S ⊆ V is called a locating dominating set, if for any two vertices v, w ∈ V − S, N (v) ∩ S = N (w) ∩ S. A locating dominating set S ⊆ V is called a co-isolated locating dominating set, if there exists atleast one isolated vertex in < V − S >. The co-isolated locating domination number γ cild is the minimum cardinality of a co-isolated locating dominating set. A graph G is called doubly-connected if both G and its complement G are connected.
Let G (V, E) be a simple, finite, undirected connected graph. A non – empty set S ⊆ V of a graph ... more Let G (V, E) be a simple, finite, undirected connected graph. A non – empty set S ⊆ V of a graph G is a dominating set, if every vertex in V – S is adjacent to atleast one vertex in S. A dominating set S ⊆ V is called a locating dominating set, if for any two vertices v, w ∈ V – S, N(v) ∩ S ≠ N(w) ∩ S. A locating dominating set S ⊆ V is called a co – isolated locating dominating set, if there exists atleast one isolated vertex in <V – S >. The co – isolated locating domination number γ cild is the minimum cardinality of a co – isolated locating dominating set. The number of minimum co – isolated locating dominating sets in a graph G is denoted by γ Dcild (G). In this paper, the number γ Dcild is obtained for a Path P n , where n ≥ 3.
Let G (V, E) be a simple, finite, undirected connected graph. A non – empty set S ⊆ V of a graph ... more Let G (V, E) be a simple, finite, undirected connected graph. A non – empty set S ⊆ V of a graph G is a dominating set, if every vertex in V – S is adjacent to atleast one vertex in S. A dominating set S ⊆ V is called a locating dominating set, if for any two vertices v, w ∈ V – S, N(v) ∩ S ≠ N(w) ∩ S. A locating dominating set S ⊆ V is called a co – isolated locating dominating set, if there exists atleast one isolated vertex in <V – S >. The co – isolated locating domination number γ cild is the minimum cardinality of a co – isolated locating dominating set. γ Dcild is the number of minimum co – isolated locating dominating set of a graph G. In this paper, the number γ Dcild is obtained for a cycle C n , n ≥ 3.
Conference Presentations by Meenal Nachiappan
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Papers by Meenal Nachiappan
Conference Presentations by Meenal Nachiappan