Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
The exact maximal energy of integral circulant graphs with prime power order
View through CrossRef
The energy of a graph was introduced by {\sc Gutman} in 1978 as the sum of the absolute values of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs, which can be characterized by their vertex count n and a set D of divisors of n in such a way that they have vertex set Z/nZ and edge set {{a,b}:a,b∈Z/nZ,gcd(a−b,n)∈D}.
Given an arbitrary prime power ps, we determine all divisor sets maximising the energy of an integral circulant graph of order ps. This enables us to compute the maximal energy \Emaxps among all integral circulant graphs of order ps.
Title: The exact maximal energy of integral circulant graphs with prime power order
Description:
The energy of a graph was introduced by {\sc Gutman} in 1978 as the sum of the absolute values of the eigenvalues of its adjacency matrix.
We study the energy of integral circulant graphs, also called gcd graphs, which can be characterized by their vertex count n and a set D of divisors of n in such a way that they have vertex set Z/nZ and edge set {{a,b}:a,b∈Z/nZ,gcd(a−b,n)∈D}.
Given an arbitrary prime power ps, we determine all divisor sets maximising the energy of an integral circulant graph of order ps.
This enables us to compute the maximal energy \Emaxps among all integral circulant graphs of order ps.
Related Results
Recognizing Circulant Graphs of Prime Order in Polynomial Time
Recognizing Circulant Graphs of Prime Order in Polynomial Time
A circulant graph $G$ of order $n$ is a Cayley graph over the cyclic group ${\bf Z}_n.$ Equivalently, $G$ is circulant iff its vertices can be ordered such that the corresponding a...
Fibonacci Prime Labelling on the Class of Flower Graphs
Fibonacci Prime Labelling on the Class of Flower Graphs
Graph labeling is one of the significant topics in graph theory. One of its interesting variants is Fibonacci prime labeling, a special type of labeling that assigns Fibonacci numb...
Independent Set in Neutrosophic Graphs
Independent Set in Neutrosophic Graphs
New setting is introduced to study neutrosophic independent number and independent neutrosophic-number arising neighborhood of different vertices. Neighbor is a key term to have th...
Failed Independent Number in Neutrosophic Graphs
Failed Independent Number in Neutrosophic Graphs
New setting is introduced to study neutrosophic failed-independent number and failed independent neutrosophic-number arising neighborhood of different vertices. Neighbor is a key t...
ADN tumoral circulant : aspects analytiques et intérêt dans la prise en charge des patients atteints de mélanome cutané métastatique
ADN tumoral circulant : aspects analytiques et intérêt dans la prise en charge des patients atteints de mélanome cutané métastatique
L'ADN tumoral circulant désigne la fraction de l'ADN circulant sanguin provenant des cellules malignes, identifiable et quantifiable par la détection d'altérations génétiques spéci...
Computing a Minimum Subset Feedback Vertex Set on Chordal Graphs Parameterized by Leafage
Computing a Minimum Subset Feedback Vertex Set on Chordal Graphs Parameterized by Leafage
Abstract
Chordal graphs are characterized as the intersection graphs of subtrees in a tree and such a representation is known as the tree model. Restricting the characteriz...
The Canberra Bubble
The Canberra Bubble
According to the ABC television program Four Corners, “Parliament House in Canberra is a hotbed of political intrigue and high tension … . It’s known as the ‘Canberra Bubble’ and i...
Exhaustive Enumeration of Spatial Prime Structures
Exhaustive Enumeration of Spatial Prime Structures
Prime structures are link chains with 0 DoF (degrees of freedom), not including subchains with 0 or fewer DoF, which are expected to be used in systematic kinematic and dynamic ana...