Jaya Gopal

Algorithms and Discrete Applied Mathematics, 2016

A locating-dominating set LDS S of a graph G is a dominating set S of G such that for every two v... more A locating-dominating set LDS S of a graph G is a dominating set S of G such that for every two vertices u and v in $$VG \setminus S$$, $$Nu\cap S \ne Nv\cap S$$. The locating-domination number $$\gamma ^{L}G$$ is the minimum cardinality of a LDS of G. Further if S is a total dominating set then S is called a locating-total dominating set. In this paper we determine the domination, total domination, locating-domination and locating-total domination numbers for hypertrees.

A locating-dominating set (LDS) S of a graph G is a dominating set S of G such that for every two... more A locating-dominating set (LDS) S of a graph G is a dominating set S of G such that for every two vertices u and v in V (G) \ S, N (u) ∩ S = N (v) ∩ S. The locating-domination number γ L (G) is the minimum cardinality of a LDS of G. Further if S is a total dominating set then S is called a locating-total dominating set. In this paper we determine the domination, total domination, locating-domination and locating-total domination numbers for hypertrees.

TIGHT LOWER BOUND FOR LOCATING-TOTAL DOMINATION NUMBER

Locating-dominating set in a connected graph G is a dominating set S of G such that for every pai... more Locating-dominating set in a connected graph G is a dominating set S of G such that for every pair of vertices u and v in V (G) \ S, N (u) ∩ S = N (v) ∩ S. Further, if S is a total dominating set, then S is called a locating-total dominating set. The locating-domination number γ L (G) is the minimum cardinality of a locating-dominating set of G and the locating-total domination number γ L t (G) is the minimum cardinality of a locating-total dominating set of G. In this paper we prove that if G is a necklace or a windmill graph, then γ L (G) = γ L t (G).

Combinatorial Properties of Root-fault Hypertrees

Combinatorial properties have become more and more important recently in the study of reliability... more Combinatorial properties have become more and more important recently in the study of reliability, fault tolerance, randomized routing, and transmission delay in interconnection networks. In this paper, we prove that hypertrees are planar. We also discuss certain combinatorial properties of root-fault hypertrees.

Algorithms and Discrete Applied Mathematics, 2016

TIGHT LOWER BOUND FOR LOCATING-TOTAL DOMINATION NUMBER

Combinatorial Properties of Root-fault Hypertrees