The Characteristic Polynomials of Symmetric Graphs

Chbili, Nafaa; Dhaheri, Shamma Al; Tahnon, Mei Y.; Abunamous, Amna A. E.

doi:10.3390/sym10110582

Cited by 3 publications

(2 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These results have been extended to the Laplacian characteristic polynomial in [24]. A similar study of the characteristic polynomial of symmetric graphs using block circulant matrices can be found in [25]. It is worth mentioning here that most of the formulas introduced in the above mentioned papers express the polynomial of the symmetric graph G in terms of the polynomial of its quotient graph G. The advantage of the conditions introduced in Theorems 1 and 2 is that they do not involve the quotient graph.…”

Section: Further Discussionmentioning

confidence: 82%

Tutte Polynomials and Graph Symmetries

et al. 2022

Self Cite

View full text Add to dashboard Cite

The Tutte polynomial is an isomorphism invariant of graphs that generalizes the chromatic and the flow polynomials. This two-variable polynomial with integral coefficients is known to carry important information about the properties of the graph. It has been used to prove long-standing conjectures in knot theory. Furthermore, it is related to the Potts and Ising models in statistical physics. The purpose of this paper is to study the interaction between the Tutte polynomial and graph symmetries. More precisely, we prove that if the automorphism group of the graph G contains an element of prime order p, then the coefficients of the Tutte polynomial of G satisfy certain necessary conditions.

show abstract

Section: Further Discussionmentioning

confidence: 82%

Tutte Polynomials and Graph Symmetries

et al. 2022

Self Cite

View full text Add to dashboard Cite

show abstract

“…However, we need information about the stabilizers of primevalent symmetric graphs and a more detailed discussion. Additionally, the term symmetric graph that is used in this paper has been also used for a different type of symmetry in other research works; see [24], for example. It studied the symmetry of graphs through characteristic polynomials, which is more interesting and detailed.…”

Section: Introductionmentioning

confidence: 99%

Classifying Seven-Valent Symmetric Graphs of Order 8pq

Jiang,

Ling,

Yang

et al. 2024

Mathematics

View full text Add to dashboard Cite

A graph is symmetric if its automorphism group is transitive on the arcs of the graph. Guo et al. determined all of the connected seven-valent symmetric graphs of order 8p for each prime p. We shall generalize this result by determining all of the connected seven-valent symmetric graphs of order 8pq with p and q to be distinct primes. As a result, we show that for each such graph of Γ, it is isomorphic to one of seven graphs.

show abstract

On Laplacian Energy of r-Uniform Hypergraphs

Yalçin

2023

Symmetry

View full text Add to dashboard Cite

The matrix representations of hypergraphs have been defined via hypermatrices initially. In recent studies, the Laplacian matrix of hypergraphs, a generalization of the Laplacian matrix, has been introduced. In this article, based on this definition, we derive bounds depending pair-degree, maximum degree, and the first Zagreb index for the greatest Laplacian eigenvalue and Laplacian energy of r-uniform hypergraphs and r-uniform regular hypergraphs. As a result of these bounds, Nordhaus–Gaddum type bounds are obtained for the Laplacian energy.

show abstract

The Characteristic Polynomials of Symmetric Graphs

Cited by 3 publications

References 6 publications

Tutte Polynomials and Graph Symmetries

Tutte Polynomials and Graph Symmetries

Classifying Seven-Valent Symmetric Graphs of Order 8pq

On Laplacian Energy of r-Uniform Hypergraphs

Contact Info

Product

Resources

About