Graph Theory and Interconnection Networks

2008 ◽  
Author(s):  
Lih-Hsing Hsu ◽  
Cheng-Kuan Lin
Keyword(s):  
Graph Theory ◽  
Interconnection Networks

THE CUBE-OF-RINGS INTERCONNECTION NETWORK

1998 ◽  
Vol 09 (01) ◽  
pp. 25-37 ◽  
Author(s):  
THOMAS J. CORTINA ◽  
ZHIWEI XU
Keyword(s):  
Graph Theory ◽  
Interconnection Networks ◽  
Fault Tolerant ◽  
Interconnection Network ◽  
Routing Algorithm ◽  
Parallel Computers ◽  
Closed Form Expression ◽  
Form Expression ◽  
Graph Theoretic ◽  
Basic Graph

We present a family of interconnection networks named the Cube-Of-Rings (COR) networks along with their basic graph-theoretic properties. Aspects of group graph theory are used to show the COR networks are symmetric and optimally fault tolerant. We present a closed-form expression of the diameter and optimal one-to-one routing algorithm for any member of the COR family. We also discuss the suitability of the COR networks as the interconnection network of scalable parallel computers.

On topological indices of poly oxide, poly silicate, DOX, and DSL networks

2015 ◽  
Vol 93 (7) ◽  
pp. 730-739 ◽  
Author(s):  
Abdul Qudair Baig ◽  
Muhammad Imran ◽  
Haidar Ali
Keyword(s):  
Molecular Structure ◽  
Graph Theory ◽  
Physicochemical Properties ◽  
Interconnection Networks ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Silicate Network ◽  
Graph Invariant ◽  
Qspr Study ◽  
Atom Bond

Topological indices are numerical parameters of a graph that characterize its topology and are usually graph invariant. In a QSAR/QSPR study, physicochemical properties and topological indices such as Randić, atom–bond connectivity (ABC), and geometric–arithmetic (GA) indices are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study different interconnection networks and derive analytical closed results of the general Randić index (Rα(G)) for α = 1, [Formula: see text], –1, [Formula: see text] only, for dominating oxide network (DOX), dominating silicate network (DSL), and regular triangulene oxide network (RTOX). All of the studied interconnection networks in this paper are motivated by the molecular structure of a chemical compound, SiO4. We also compute the general first Zagreb, ABC, GA, ABC4, and GA5 indices and give closed formulae of these indices for these interconnection networks.

scholarly journals On topological properties of block shift and hierarchical hypercube networks

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 810-819
Author(s):  
Juan Luis García Guirao ◽  
Muhammad Kamran Siddiqui ◽  
Asif Hussain
Keyword(s):  
Graph Theory ◽  
Interconnection Networks ◽  
Communication Theory ◽  
Chemical Reactivity ◽  
Zagreb Index ◽  
Electronic Engineering ◽  
Chemical Graph Theory ◽  
Chemical Constitution ◽  
Vertex Degrees ◽  
Hypercube Networks

Abstract Networks play an important role in electrical and electronic engineering. It depends on what area of electrical and electronic engineering, for example there is a lot more abstract mathematics in communication theory and signal processing and networking etc. Networks involve nodes communicating with each other. Graph theory has found a considerable use in this area of research. A topological index is a real number associated with chemical constitution purporting for correlation of chemical networks with various physical properties, chemical reactivity. The concept of hyper Zagreb index, first multiple Zagreb index, second multiple Zagreb index and Zagreb polynomials was established in chemical graph theory based on vertex degrees. In this paper, we extend this study to interconnection networks and derive analytical closed results of hyper Zagreb index, first multiple Zagreb index, second multiple Zagreb index, Zagreb polynomials and redefined Zagreb indices for block shift network (BSN − 1) and (BSN − 2), hierarchical hypercube (HHC − 1) and (HHC − 2).

scholarly journals A new characterization and a recognition algorithm of Lucas cubes

2013 ◽  
Vol Vol. 15 no. 3 (Graph Theory) ◽  
Author(s):  
Andrej Taranenko
Keyword(s):  
Graph Theory ◽  
Interconnection Networks ◽  
Linear Time ◽  
Recognition Algorithm ◽  
Induced Subgraphs ◽  
Fibonacci Cube ◽  
Vertex Set ◽  
International Audience ◽  
Binary Strings

Graph Theory International audience Fibonacci and Lucas cubes are induced subgraphs of hypercubes obtained by excluding certain binary strings from the vertex set. They appear as models for interconnection networks, as well as in chemistry. We derive a characterization of Lucas cubes that is based on a peripheral expansion of a unique convex subgraph of an appropriate Fibonacci cube. This serves as the foundation for a recognition algorithm of Lucas cubes that runs in linear time.

scholarly journals An Approach to the Geometric-Arithmetic Index for Graphs under Transformations’ Fact over Pendent Paths

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Muhammad Asif ◽  
Hamad Almohamedh ◽  
Muhammad Hussain ◽  
Khalid M Alhamed ◽  
Abdulrazaq A. Almutairi ◽  
...  
Keyword(s):  
Graph Theory ◽  
Computer Science ◽  
Connected Graph ◽  
Interconnection Networks ◽  
Extremal Graphs ◽  
Graph Invariant ◽  
Fully Connected ◽  
New Inequalities

Graph theory is a dynamic tool for designing and modeling of an interconnection system by a graph. The vertices of such graph are processor nodes and edges are the connections between these processors nodes. The topology of a system decides its best use. Geometric-arithmetic index is one of the most studied graph invariant to characterize the topological aspects of underlying interconnection networks or graphs. Transformation over graph is also an important tool to define new network of their own choice in computer science. In this work, we discuss transformed family of graphs. Let Γ n k , l be the connected graph comprises by k number of pendent path attached with fully connected vertices of the n-vertex connected graph Γ . Let A α Γ n k , l and A α β Γ n k , l be the transformed graphs under the fact of transformations A α and A α β , 0 ≤ α ≤ l , 0 ≤ β ≤ k − 1 , respectively. In this work, we obtained new inequalities for the graph family Γ n k , l and transformed graphs A α Γ n k , l and A α β Γ n k , l which involve GA Γ . The presence of GA Γ makes the inequalities more general than all those which were previously defined for the GA index. Furthermore, we characterize extremal graphs which make the inequalities tight.

A Brief Account on the Development and Future Research Directions of Connectivity Properties of Interconnection Networks

2020 ◽  
Vol 30 (03) ◽  
pp. 2040009
Author(s):  
Eddie Cheng ◽  
Ke Qiu ◽  
Zhizhang Shen ◽  
Weihua Yang
Keyword(s):  
Graph Theory ◽  
Interconnection Networks ◽  
Future Research ◽  
Research Directions ◽  
Short Commentary ◽  
Future Research Directions

Connectivity type measures form an important topic in graph theory. Such measures provide an important part of analyzing the vulnerability and resilience of interconnection networks. In this short commentary, we outline our perspective on the development of this topic with respect to interconnection networks.

scholarly journals Strategies for interconnection networks: Some methods from graph theory

1986 ◽  
Vol 3 (4) ◽  
pp. 433-449 ◽  
Author(s):  
J.-C. Bermond ◽  
C. Delorme ◽  
J.-J. Quisquater
Keyword(s):  
Graph Theory ◽  
Interconnection Networks
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