simon raj f | Hindustan University (original) (raw)

Papers by simon raj f

In this paper, we have introduced few Interconnection Networks, called David Derived Network DD(n... more In this paper, we have introduced few Interconnection Networks, called David Derived Network DD(n) , Dominating David Derived Network DDD(n), Honeycomb cup Network HCC(n) and Kite Regular Trianguline Mesh KRrTM(n). We have given drawing algorithm for DDD(n) from Honeycomb network HC(n) and embedded poly–Honeycomb Networks, KRrTM(n) in to Dominating David Derived Networks. Also we have investigated the metric dimension of Star of David network SD(n) and lower bound of the metric dimension for DD(n).

Let M = {m1, m2,…, mp} be an ordered set of vertices in a graph G(V, E). Then (d(u, m1), d(u, m2)... more Let M = {m1, m2,…, mp} be an ordered set of vertices in a graph G(V, E). Then (d(u, m1), d(u, m2),…, d(u, mp)) is called the p-dimensional vector of distances coordinate or p-coordinate of a vertex u of G. The set M is called a resolving set if the vertices of G have distinct p-coordinate. A metric basis is a resolving set M with minimum cardinality. If M is a metric basis then it is clear that for each pair of vertices u and v in the set of vertices V of G not in M, there is a vertex m in M such that the distance between u and m is not equal to the distance between v and m. The cardinality of a metric basis of G is called metric dimension. The members of a metric basis are called landmarks. A metric dimension problem is to find a metric basis. The problem of finding metric dimension is an NP Complete for general graphs. In this paper we have derived certain new networks called Hex derived network three HDN 3 and Poly (Triangular and Rectangular) Hex derived network three PHDN 3 fro...

A minimum resolving set or a metric basis M for a graph G(V, E) is a small subset of vertices of ... more A minimum resolving set or a metric basis M for a graph G(V, E) is a small subset of vertices of V such that for every pair of vertices x and y of V \ M, there exist at least one vertex m in M such that the distance between x and m is not equal to the distance between y and m. The number of elements of the metric basis M of G is called metric dimension and the elements of a metric basis are called landmarks. A metric dimension problem for a graph G is to find a metric basis for G. In this paper a new silicate graph called Silicate Stars or Star of Silicate Networks SSL(n) has been derived from Star of David Networks SD(n). The metric dimension problem has been solved for SSL(n) , Single Oxide chain, and single Silicate chain. The problem of finding the metric dimension of a general graph is an NP Complete Problem.

International Journal of Computer Mathematics: Computer Systems Theory

September, 2019

Let be a vertex of a connected simple graph and be a pair of vertices in G. let) be the distance ... more Let be a vertex of a connected simple graph and be a pair of vertices in G. let) be the distance between and A vertex is said to resolve and if. A set of vertices W of G is called a settling set of Gif every pair of vertices resolved by atleast one vertices. A settling set of G with least cardinality is called metric premise of G. The cardinality of metric premise is called metric index of G. In this paper metric index of oxide network is investigated.

International Journal of Innovative Technology and Exploring Engineering

Let be a vertex of a connected simple graph and be a pair of vertices in G. let ) be the distance... more Let be a vertex of a connected simple graph and be a pair of vertices in G. let ) be the distance between and A vertex is said to resolve and if . A set of vertices W of G is called a settling set of Gif every pair of vertices resolved by atleast one vertices . A settling set of G with least cardinality is called metric premise of G. The cardinality of metric premise is called metric index of G. In this paper metric index of oxide network is investigated.

2015 IEEE International Conference on Electrical, Computer and Communication Technologies (ICECCT), 2015

ABSTRACT An important feature of an interconnection network is its ability to efficiently simulat... more ABSTRACT An important feature of an interconnection network is its ability to efficiently simulate programs written for other architectures. Such a simulation problem can be mathematically formulated as graph embedding. Graph embedding is an important technique for studying computational capabilities of processor interconnection networks and task distributions , which is a recent focus of research in the parallel processing area. This paper, deal with embedding of hexagonal networks , honeycomb networks , Silicate networks , Oxide networks, and certain Nanosheet in to Planar Octahedron networks.

Meshes and tori are widely used topologies for Network on chip (NoC). In this paper a new planar ... more Meshes and tori are widely used topologies for Network on chip (NoC). In this paper a new planar architecture called Hexagonal cage network HXCa(n) with two layers derived using two hexagonal meshes of same dimension. And a Hamiltonian cycle is shown in HXCa(4). In the last section a new operation called " Boundary vertex connection " (BVC) is introduced and conjectured that BVC of a 2-connected plane graph is Hamiltonian. For an ordered set M={m1,m2,m3,…,mp} of vertices in a connected graph G and a vertex u of G, the code of u with respect to M is the p-dimensional distance vector CM (u) = (d(v, m1), d(v, m2), d(v, m3),…,d(v, mp)). The set M is called the resolving set for G if d(x, m) ≠ d(y, m) for x, y in V \ M and m in M. A resolving set of minimum cardinality is called a minimum resolving set or a metric basis for G. The cardinality of the metric basis is called the metric dimension of G and is denoted by dim(G). In this paper the metric dimension problem is investigated for HXCa(n) Finding a metric basis and Hamiltonian cycle in a arbitrary graph is NP hard problem.

Let M = {v1, v2,…, vn} be an ordered set of vertices in a graph G(V,E). Then (d(u, v1), d(u, v2),... more Let M = {v1, v2,…, vn} be an ordered set of vertices in a graph G(V,E). Then (d(u, v1), d(u, v2),...d(u, vn)) is called the M-coordinates of a vertex u of G. The set M is called a resolving set if the vertices of G have distinct M-coordinates. A metric basis is a resolving set M with minimum cardinality. If M is a metric basis then it is clear that for each pair of vertices u and v in the set of vertices V of G not in M, there is a vertex m in M such that the distance between u and m is not equal to the distance between v and m. The cardinality of a metric basis of G is called metric dimension. The members of a metric basis are called landmarks. A metric dimension problem is to find a metric basis. The problem of finding metric dimension is an NP-Complete for general graphs. In this paper we have studied the metric dimension of a new graph called Octo–Nano windows , HDN like networks namely Equilateral Triangular Tetra sheets and Rectangular Tetra Sheet networks.

This paper deals with a new interconnection network motivated by molecular structure of a chemica... more This paper deals with a new interconnection network motivated by molecular structure of a chemical compound SiO4. The different forms of silicate available in nature lead to the introduction of the Dominating silicate network(DSL). The first section deals with the introduction to the metric dimension problems, and few related work about Silicate networks. The second section introduces and gives an account of the proof to the topological properties of poly-Oxide, Poly-Silicate, Dominating Oxide (DOX), Dominating Silicate networks, and Regular Triangulene Oxide network (RTOX). The third section deals with the drawing algorithm for dominating silicate networks, and shown complete embedding of Oxide and Silicate network in to Dominating Oxide and Dominating Silicate network respectively. The fourth section contains the proof of the metric dimension of Regular Triangulene oxide network to be 2.

International Journal of Computer Mathematics: Computer Systems Theory

September, 2019

International Journal of Innovative Technology and Exploring Engineering

Let be a vertex of a connected simple graph and be a pair of vertices in G. let ) be the distance... more Let be a vertex of a connected simple graph and be a pair of vertices in G. let ) be the distance between and A vertex is said to resolve and if . A set of vertices W of G is called a settling set of Gif every pair of vertices resolved by atleast one vertices . A settling set of G with least cardinality is called metric premise of G. The cardinality of metric premise is called metric index of G. In this paper metric index of oxide network is investigated.

2015 IEEE International Conference on Electrical, Computer and Communication Technologies (ICECCT), 2015