The trace and Estrada index of uniform hypergraphs with cut vertices

Fan, Yi-Zheng; Yang, Yong; She, Chuan-Ming; Zheng, Jinhai; Song, Yimin; Yang, Hongxia

doi:10.1016/j.laa.2022.12.006

Cited by 2 publications

(3 citation statements)

References 39 publications

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“…As R(F ) is Eulerian, τ u (R(F )) is independent of the choice of the root u so that the root u is omitted. Fan et al [20] give an expression of the d-th trace of H as follows.…”

Section: Tracesmentioning

confidence: 99%

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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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“…As R(F ) is Eulerian, τ u (R(F )) is independent of the choice of the root u so that the root u is omitted. Fan et al [20] give an expression of the d-th trace of H as follows.…”

Section: Tracesmentioning

confidence: 99%

“…Lemma 4 [20]. Let H be an m-uniform Veblen multi-hypergraph whose underlying hypergraph H is a hypertree.…”

Section: Traces Of Hypertreesmentioning

confidence: 99%

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High-ordered spectral characterization of unicyclic graphs

Fan¹,

Yang²,

Zheng³

2024

Discuss. Math. Graph Theory

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The trace of uniform hypergraphs with application to Estrada index

Fan¹,

Zheng²,

Yang³

2023

Discrete Math. Algorithm. Appl.

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In this paper, we investigate the traces of the adjacency tensor of uniform hypergraphs (simply called the traces of hypergraphs). We give new expressions for the traces of hypertrees and linear unicyclic hypergraphs by the weight function assigned to their connected sub-hypergraphs, and present some perturbation results for the traces of a hypergraph when its structure is locally changed. As an application we determine the unique hypertree with maximum Estrada index among all hypertrees with perfect matchings and given number of edges, and the unique unicyclic hypergraph with maximum Estrada index among all unicyclic hypergraph with girth [Formula: see text] and given number of edges.

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The trace and Estrada index of uniform hypergraphs with cut vertices

Cited by 2 publications

References 39 publications

High-ordered spectral characterization of unicyclic graphs

High-ordered spectral characterization of unicyclic graphs

The trace of uniform hypergraphs with application to Estrada index

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