The Construction of Cospectral Composite Graphs

Schwenk, Allen J.; Ellzey, M. L.

doi:10.1111/j.1749-6632.1979.tb32826.x

Cited by 22 publications

(9 citation statements)

References 8 publications

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“…1967 many examples of cospectral graphs were found. One result standing out is due to Schwenk [21], who stated that almost all trees are not determined by their spectrum.…”

Section: Pmentioning

confidence: 99%

Graphs and finite geometries

Blázsik¹

2019

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First and foremost, I am most grateful to my supervisor, Tamás Szőnyi, who helped me all the time by sharing his profound knowledge of finite geometry. He was so kind to spend countless hours with me providing guidance, suggesting new ideas which most of the time turned out to be essential ones. It has been a real privilege to be a student of Tamás Szőnyi.Besides Tamás, I am truly thankful to Zoltán Lóránt Nagy, who serves as a role model for me in many ways. On several occasions, he introduced me to new problems most of which I found extremely exciting, furthermore, his solid work ethic have been an example for me to follow. Zoltán also helped me tremendously by sharing his valuable insights about writing a paper.Without the help of György Kiss, I have not been able to take part in a wonderful research program at the Fields Institute in Toronto, Canada during my undergraduate years. I have learnt a lot there, not just the way of doing research in mathematics but to work in a team, communicating better and presenting in front of an illustrious audience. I will forever be indebted to him for this incredible opportunity. This experience, together with the fascinating lectures of the Finite Geometry Seminar got me interested in doing research in general.I would like to thank every current and past member of the MTA-ELTE Geometric and Algebraic Combinatorics Research Group for the excellent atmosphere and the stimulating discussions. It is a pleasure to work with such a friendly and helpful group of people.

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“…1967 many examples of cospectral graphs were found. One result standing out is due to Schwenk [21], who stated that almost all trees are not determined by their spectrum.…”

Section: Pmentioning

confidence: 99%

Graphs and finite geometries

Blázsik¹

2019

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“…It is routine to verify that QAQ-l = A', and so this proves Theorem 1.5.4(i). D Theorem 1.5.5 (Schwenk, Herndon, and Ellzey [234]) If Gl is a regular graph and if IV(Gdl = 21Tl l, then B(Gl ,Tl ,G2,T2) and B(Gl , V(Gd -TI,G2,T2) have the same spectrum.…”

Section: 2··· Nomentioning

confidence: 99%

Matrices in Combinatorics and Graph Theory

Liu¹,

Lai²

2000

Network Theory and Applications

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“…In 1957, Collatz and Sinogowitz [10] presented a pair of non-isomorphic cospectral trees. In 1973, Schwenk [36] proved that almost every tree has a cospectral mate by constructing a non-isomorphic cospectral tree for each tree of sufficiently large order. In 1982, Godsil and McKay [24] invented a powerful method called GM-switching, which can produce lots of pairs of cospectral graphs.…”

Section: Introductionmentioning

confidence: 99%

High-ordered spectral characterization of unicyclic graphs

Fan¹,

Yang²,

Zheng³

2024

Discuss. Math. Graph Theory

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In this paper we will apply the tensor and its traces to investigate the spectral characterization of unicyclic graphs. Let G be a graph and G m be the m-th power (hypergraph) of G. The spectrum of G is referring to its adjacency matrix, and the spectrum of G m is referring to its adjacency tensor. The graph G is called determined by high-ordered spectra (DHS, for short) if, whenever H is a graph such that H m is cospectral with G m for all m, then H is isomorphic to G. In this paper we first give formulas for the traces of the power of unicyclic graphs, and then provide some high-ordered cospectral invariants of unicyclic graphs. We prove that a class of unicyclic graphs with cospectral mates is DHS, and give two examples of infinitely many pairs of cospectral unicyclic graphs but with different high-ordered spectra.

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The Construction of Cospectral Composite Graphs

Cited by 22 publications

References 8 publications

Graphs and finite geometries

Graphs and finite geometries

Matrices in Combinatorics and Graph Theory

High-ordered spectral characterization of unicyclic graphs

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