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Constructing cospectral graphs

WebAbstract We present a new method to construct a family of co-spectral graphs. Our method is based on a new type of graph product that we define, the bipartite graph product, which may be of self-interest. Our method is different from existing techniques in the sense that it is not based on a sequence of local graph operations (e.g. Godsil–McKay … WebJan 18, 2024 · Eigenvalues of signed graphs. Signed graphs have their edges labeled either as positive or negative. denote the -spectral radius of , where is a real symmetric graph matrix of . Obviously, . Let be the adjacency matrix of and be a signed complete graph whose negative edges induce a subgraph .

Constructing cospectral signed graphs - Taylor & Francis

WebSome new constructions for families of cospectral graphs are derived, and some old ones are considerably generalized. One of our new constructions is sufficiently powerful to produce an estimated 72% of the 51039 graphs on 9 vertices which do not have unique … WebA well-known fact in Spectral Graph Theory is the existence of pairs of cospectral (or isospectral) nonisomorphic graphs, known as PINGS. The work of A.J. Schwenk (in 1973) and of C. Godsil and B. McKay (in 1982) shed some light on the explanation of the presence of cospectral graphs, and they gave routines to construct PINGS. o-woche passau https://pineleric.com

Constructing cospectral signed graphs - Taylor & Francis

WebSeidel switching is an operation on graphs G satisfying certain regularity properties so that the resulting graph H has the same spectrum as G . If G is simple then the complement of G and the complement of H are also cospectral. We use a generalization ... WebFeb 15, 2024 · Constructing cospectral signed graphs. F. Belardo, M. Brunetti, Matteo Cavaleri, A. Donno; Mathematics. Linear and Multilinear Algebra. 2024; ABSTRACT A well-known fact in Spectral Graph Theory is the existence of pairs of cospectral (or isospectral) nonisomorphic graphs, known as PINGS. WebConstructing cospectral graphs. Constructing cospectral graphs. Chris Godsil. 1982, Aequationes Mathematicae. DigiZeitschriften e.V. gewährt ein nicht exklusives, nicht übertragbares, persönliches und beschränktes Recht auf Nutzung dieses Dokuments. Dieses Dokument ist ausschließlich für den persönlichen, nicht kommerziellen Gebrauch ... o-works ss 2.0 グリップ red/black

Large Families of Cospectral Graphs Designs, Codes and …

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Constructing cospectral graphs

A switching method for constructing cospectral gain graphs

http://users.cecs.anu.edu.au/~bdm/papers/GodsilMcKayCospectral.pdf WebApr 7, 2024 · A switching method for constructing cospectral gain graphs. A gain graph over a group , also referred to as -gain graph, is a graph where an element of a group , called gain, is assigned to each oriented edge, in such a way that the inverse element is associated with the opposite orientation. Gain graphs can be regarded as a …

Constructing cospectral graphs

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WebApr 10, 2024 · and (Γ2,ψ2) are G-cospectral if any only if they are π-cospectral for every unitary repre-sentation πof G. This way, G-cospectrality is a more general notion than π-cospectrality. 3 A switching to construct G-cospectral gain graphs The main goal of this section is to show a new method to obtain pairs of G-cospectral gain graphs. WebIn this work we propose methods to construct cospectral graphs by utilizing the framework of clustered graphs. A graph G = (V, E) with labellings on vertices is called clustered (also called partitioned) if the vertex set is partitioned as V = n j=1 C j where each C j , along with the edge set induced by the vertices in it, is called a cluster of the graph.

WebMar 24, 2024 · Cospectral graphs, also called isospectral graphs, are graphs that share the same graph ... WebOct 1, 2024 · Constructing cospectral non-isomorphic graphs provides valuable insights to understanding the above question. For an instance, a famous result on cospectral …

WebApr 11, 2024 · Gain graphs can be regarded as a generalization of signed graphs, among others. In this work, we show a new switching method to construct cospectral gain … WebApr 7, 2024 · graphs [3] and complex unit graphs [4], and more recently, also to ga in graphs ov er an arbitrary group [8]. The W QH-switching has also been extended, in its …

WebAug 6, 2024 · Constructing cospectral signed graphs. A well--known fact in Spectral Graph Theory is the existence of pairs of isospectral nonisomorphic graphs (known as PINGS). The work of A.J. Schwenk (in 1973) and of C. Godsil and B. McKay (in 1982) shed some light on the explanation of the presence of isospectral graphs, and they gave …

WebOct 15, 2024 · The rest of the paper is organized as follows. In Section 2, we give a new method for constructing cospectral graphs which is analogous to the GM-switching method. In Section 3, we present a family of infinitely many cospectral graphs by using the new method, which cannot be obtained from the original GM-switching. Conclusions are … jeans combination with white shirtWebDec 1, 1982 · Constructing cospectral non-isomorphic graphs has been investigated for many years and various constructions are known in the literature, among which, the GM … jeans converse shoesWebApr 11, 2024 · Gain graphs can be regarded as a generalization of signed graphs, among others. In this work, we show a new switching method to construct cospectral gain graphs. Some previous methods known for graph … jeans company logoWebJan 1, 2024 · Two graphs G and H are cospectral if they share the same spectrum. Constructing cospectral non-isomorphic graphs has been investigated for many years and various constructions are known in the literature, among which, the GM-switching, invented by Godsil and McKay in 1982, is proved to a simple and powerful one. jeans coolsculptingWebA well-known fact in Spectral Graph Theory is the existence of pairs of cospectral (or isospectral) nonisomorphic graphs, known as PINGS. The work of A.J. Schwenk (in … jeans con botasWebJul 2, 2016 · The operation of constructing \tilde {\Gamma } from \Gamma is called Godsil–McKay switching. Godsil–McKay switching has been known for years, as a method to construct cospectral graphs. However, finding an instance for which the hypotheses of Godsil–McKay switching are satisfied, is nontrivial. We mention recent work [ 1, 2 ], but … jeans corti con tasche lateraliWebA switching method for constructing cospectral gain graphs. Decentralized Proximal Optimization Method with Consensus Procedure. Additivity of multiplicative (generalized) skew semi-derivations on rings. jeans cotton and wool fabric