A locating-dominating set (LDS) 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 γL(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 and sibling trees. © 2020 Elsevier B.V.

Indra Rajasingh

Mathematics

School of Advanced Sciences

Chennai Campus

Jayagopal R

R. Sundara Rajan

Fulltext

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VIT University

Discrete Applied Mathematics

In this paper we obtain a sharp (improved) lower bound on the locatingtotal domination number of a graph, and show that the decision problem for the locating-total domination is NP-complete.

Discussiones Mathematicae Graph Theory

A note on the locating-total domination in graphs

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. © 2015 The Authors. Published by Elsevier B.V.

Journal	Data powered by TypesetDiscrete Applied Mathematics
Publisher	Data powered by TypesetElsevier BV
ISSN	0166-218X
Open Access	Yes