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Signless Laplacian Estrada index and Laplacian Estrada index of uniform hypergraphs

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Cunxiang Duan, Edwin R. van Dam, Ligong Wang

Combinatorics · Submitted 22 May 2022

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim For an $r$-uniform hypergraph $H,$ we derive an order $r+1$ trace formula of the (signless) Laplacian tensor of $H.$ Among others by using this trace formula, we obtain lower bounds for the signless Laplacian Estrada index and upper bounds for the Laplacian Estrada index.

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arXiv ID2206.00109 (version 1)
Pith IDVXQBTEMH, Pith's permanent record of this paper and its review
CitationCunxiang Duan, Edwin R. van Dam, Ligong Wang. "Signless Laplacian Estrada index and Laplacian Estrada index of uniform hypergraphs." arXiv:2206.00109 (2022). https://pith.science/paper/VXQBTEMH
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,035 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.84 · compares with prior results 0.09 · mentions code or data availability 0.01.

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arXiv listing abstract v1. Results and the main claim are underlined; .

We generalize the notions of Laplacian and signless Laplacian Estrada index to uniform hypergraphs. For an $r$-uniform hypergraph $H,$ we derive an order $r+1$ trace formula of the (signless) Laplacian tensor of $H.$ Among others by using this trace formula, we obtain lower bounds for the signless Laplacian Estrada index and upper bounds for the Laplacian Estrada index. Moreover, we establish a bound involving both the Laplacian Estrada index and Laplacian energy of a uniform hypergraph.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We generalize the notions of Laplacian and signless Laplacian Estrada index to uniform hypergraphs. contribution 1.00 0.94 0.17 asserted 1.00
s1 For an $r$-uniform hypergraph $H,$ we derive an order $r+1$ trace formula of the (signless) Laplacian tensor of $H.$ Among others by using this trace formula, we obtain lower bounds for the signless Laplacian Estrada index and upper bounds for the Laplacian Estrada index. contribution 0.55 0.97 0.39 asserted 1.00
s2 Moreover, we establish a bound involving both the Laplacian Estrada index and Laplacian energy of a uniform hypergraph. result 0.84 0.96 0.19 asserted 1.00

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Original abstract

We generalize the notions of Laplacian and signless Laplacian Estrada index to uniform hypergraphs. For an $r$-uniform hypergraph $H,$ we derive an order $r+1$ trace formula of the (signless) Laplacian tensor of $H.$ Among others by using this trace formula, we obtain lower bounds for the signless Laplacian Estrada index and upper bounds for the Laplacian Estrada index. Moreover, we establish a bound involving both the Laplacian Estrada index and Laplacian energy of a uniform hypergraph.

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