Bounds for the Eigen Values and Energy of Degree Product Adjacency Matrix of A Graph

2019 ◽  
Vol 10 (3) ◽  
pp. 565-573
Author(s):  
Keerthi G. Mirajkar ◽  
Bhagyashri R. Doddamani
Keyword(s):  
Adjacency Matrix ◽  
Eigen Values

scholarly journals Bounds of Laplacian Energy of a Hypercube Graph

2018 ◽  
Vol 7 (4.10) ◽  
pp. 582
Author(s):  
K. Ameenal Bibi ◽  
B. Vijayalakshmi ◽  
R. Jothilakshmi
Keyword(s):  
Lower Bounds ◽  
Adjacency Matrix ◽  
Laplacian Matrix ◽  
Positive Semidefinite ◽  
Laplacian Energy ◽  
Eigen Values ◽  
Degree Matrix

Let  Qn denote  the n – dimensional  hypercube  with  order   2n and  size n2n-1. The  Laplacian  L  is defined  by  L = D  where D is  the  degree  matrix and  A is  the  adjacency  matrix  with  zero  diagonal  entries.  The  Laplacian  is a  symmetric  positive  semidefinite.  Let  µ1 ≥ µ2 ≥ ....µn-1 ≥ µn = 0 be the eigen values of  the Laplacian matrix.  The  Laplacian  energy is defined as  LE(G) = . In  this  paper, we  defined  Laplacian  energy  of  a  Hypercube  graph  and  also attained  the  lower  bounds.   

Identification of kinematic chains and distinct mechanisms using extended adjacency matrix

2007 ◽  
Vol 221 (1) ◽  
pp. 81-88 ◽  
Author(s):  
A Mohammad ◽  
R A Khan ◽  
V P Agrawal
Keyword(s):  
Adjacency Matrix ◽  
Kinematic Chain ◽  
Theoretic Approach ◽  
Kinematic Chains ◽  
Graph Theoretic ◽  
The Past ◽  
Graph Theoretic Approach ◽  
The Family ◽  
Eigen Value ◽  
Eigen Values

Development of the methods for generating distinct mechanisms derived from a given family of kinematic chains has been persued by a number of researchers in the past, as the distinct kinematic structures provide distinct performance characteristics. A new method is proposed to identify the distinct mechanisms derived from a given kinematic chain in this paper. Kinematic chains and their derived mechanisms are represented in the form of an extended adjacency matrix [EA] using the graph theoretic approach. Two structural invariants derived from the eigen spectrum of the [EA] matrix are the sum of absolute eigen values EA∑ and maximum absolute eigen value EAmax. These invariants are used as the composite identification number of a kinematic chain and mechanism and are tested to identify the all-distinct mechanisms derived from the family of 1-F kinematic chains up to 10 links. The identification of distinct kinematic chains and their mechanisms is necessary to select the best possible mechanism for the specified task at the conceptual stage of design.

scholarly journals A Note on Skew Energy of Hadamard Graph

2019 ◽  
Vol 9 (1S4) ◽  
pp. 1010-1013
Keyword(s):  
Adjacency Matrix ◽  
Oriented Graph ◽  
Eigen Values ◽  
Skew Energy ◽  
The Absolute

The skew spectrum and skew energy of an oriented graph are respectively the set of eigenvalues of the adjacency matrix of and the sum of the absolute values of the eigen values of the adjacency matrix of . In this work, we find and study the skew spectrum and the skew energy of Hadamard graph for a particular orientation.

scholarly journals The Energy of Conjugacy Classes Graphs of Some Order of Alternating Groups

2020 ◽  
Vol 7 (4) ◽  
pp. 62-71
Author(s):  
Zuzan Naaman Hassan ◽  
Nihad Titan Sarhan
Keyword(s):  
Conjugacy Class ◽  
Adjacency Matrix ◽  
Finite Graph ◽  
Conjugacy Classes ◽  
Alternating Group ◽  
Alternating Groups ◽  
Eigen Values ◽  
Finite Set ◽  
Class Graph ◽  
Square Matrix

The energy of a graph , is the sum of all absolute values of the eigen values of the adjacency matrix which is indicated by . An adjacency matrix is a square matrix used to represent of finite graph where the rows and columns consist of 0 or 1-entry depending on the adjacency of the vertices of the graph. The group of even permutations of a finite set is known as an alternating group  . The conjugacy class graph is a graph whose vertices are non-central conjugacy classes of a group , where two vertices are connected if their cardinalities are not coprime. In this paper, the conjugacy class of alternating group  of some order for   and their energy are computed. The Maple2019 software and Groups, Algorithms, and Programming (GAP) are assisted for computations.

scholarly journals A review on eigen values of adjacency matrix of graph with cliques

2017 ◽  
Author(s):  
Ema Carnia ◽  
Moch. Suyudi ◽  
Isah Aisah ◽  
Asep K. Supriatna
Keyword(s):  
Adjacency Matrix ◽  
Eigen Values

ON LOWER BOUNDS FOR THE COMMUNICATION VOLUME IN DISTRIBUTED SYSTEMS

1991 ◽  
Vol 01 (02) ◽  
pp. 125-133
Author(s):  
U. A. RANAWAKE ◽  
P. M. LENDERS ◽  
S. M. GOODNICK
Keyword(s):  
Distributed Systems ◽  
Lower Bound ◽  
Lower Bounds ◽  
Adjacency Matrix ◽  
Task Graph ◽  
Task Graphs ◽  
Total Communication ◽  
Eigen Values

In this paper we derive a lower bound for the total communication volume when mapping arbitrary task graphs onto a distributed processor system. For a K processor system this lower bound can be computed with only the K (possibly) largest eigen values of the adjacency matrix of the task graph and the eigen values of the adjacency matrix of the processor graph. We also derive the eigen values of the adjacency matrix of the processor graph for a hypercube multiprocessor and illustrate the concept with a simple example for the two processor case.

scholarly journals Dominating Energy in Neutrosophic graphs

2020 ◽  
pp. 38-58
Author(s):  
M. Mullai ◽  
◽  
◽  
Said Broumi
Keyword(s):  
Graph Theory ◽  
Adjacency Matrix ◽  
Vital Role ◽  
Eigen Values ◽  
Neutrosophic Graph

Dominating energy of graphs plays a vital role in the field of application in energy. Results by applying neutrosophic graph theory is more efficient than other existing methods. So, dominating energy of neutrosophic graphs will also give more accurate results than other exixting methods in the field of energy. This article introduces dominating energy of neutrosophic graphs. Dominating energy of a neutrosophic graph, dominating neutrosophic adjacency matrix, eigen values for the dominating energy of a neutrosophic graphs and complement of neutrosophic graphs are defined with examples. Also, dominating energy in union and join operations of neutrosophic graphs are developed and some theorems in dominating energy of a neutrosophic graphs are derived here.

Energy of spherical fuzzy graphs

2020 ◽  
pp. 321-332
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Adjacency Matrix ◽  
Upper Bounds ◽  
Fuzzy Graph ◽  
Lower And Upper Bounds ◽  
Fuzzy Graphs

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.

Mathematics of networks

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Random Walks ◽  
Adjacency Matrix ◽  
Graph Partitioning ◽  
Dynamic Networks ◽  
Graph Laplacian ◽  
Network Visualization ◽  
Final Part ◽  
Bipartite Networks ◽  
Component Structure ◽  
Basic Properties

An introduction to the mathematical tools used in the study of networks. Topics discussed include: the adjacency matrix; weighted, directed, acyclic, and bipartite networks; multilayer and dynamic networks; trees; planar networks. Some basic properties of networks are then discussed, including degrees, density and sparsity, paths on networks, component structure, and connectivity and cut sets. The final part of the chapter focuses on the graph Laplacian and its applications to network visualization, graph partitioning, the theory of random walks, and other problems.

scholarly journals A Note on the Estrada Index of the Aα-Matrix

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 811
Author(s):  
Jonnathan Rodríguez ◽  
Hans Nina
Keyword(s):  
Lower Bounds ◽  
Adjacency Matrix ◽  
Estrada Index

Let G be a graph on n vertices. The Estrada index of G is an invariant that is calculated from the eigenvalues of the adjacency matrix of a graph. V. Nikiforov studied hybrids of A(G) and D(G) and defined the Aα-matrix for every real α∈[0,1] as: Aα(G)=αD(G)+(1−α)A(G). In this paper, using a different demonstration technique, we present a way to compare the Estrada index of the Aα-matrix with the Estrada index of the adjacency matrix of the graph G. Furthermore, lower bounds for the Estrada index are established.

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