Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

&nbsp;

&nbsp;

VIT University

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.

Mathematics

School of Advanced Sciences

Chennai Campus

World University root node

Fulltext

Discrete Applied Mathematics

Domination parameters in hypertrees and sibling trees

In this paper, we introduce a new form of fuzzy number named as Icosikaitetragonal fuzzy number with its membership function. It includes some basic arithmetic operations like addition, subtraction, multiplication and scalar multiplication by means of a-cut with numerical illustrations. © 2020 Charles Babbage Research Centre. All rights reserved.

Journal of Combinatorial Mathematics and Combinatorial Computing

A new operation on icosikaitetragonal fuzzy number

A set S of vertices in a graph G is said to be a dominating set if every vertex in V(G) \Sis adjacent to some vertex in S. A dominating set S is called a total dominating set if each vertex of V(G) is adjacent to some vertex in S. Molecules arranging themselves into predictable patterns on silicon chips could lead to microprocessors with much smaller circuit elements. Mathematically, assembling in predictable patterns is equivalent to packing in graphs. In this paper, we determine the total domination number for certain nanotori using packing as a tool. © 2020 Charles Babbage Research Centre. All rights reserved.

Total domination in certain nanotori

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

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 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. © Springer International Publishing Switzerland 2016.

Algorithms and Discrete Applied Mathematics Lecture Notes in Computer Science

Domination Parameters in Hypertrees

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.

VIT Unitversity

Procedia Computer Science

Combinatorial Properties of Root-fault Hypertrees

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 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 parameters for corona graph. © Research India Publications.

International Journal of Applied Engineering Research

Domination parameters in corona graph

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 6= N(v) S. Further, if S is a total dominating set, then S is called a locatingtotal dominating set. The locating-domination number L(G) is the minimum cardinality of a locating-dominating set of G and the locating-total domination number 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 L(G) = L t (G). © 2015 Academic Publications, Ltd.