For any finite, undirected, non-bipartite, vertex-transitive graph, we establish an explicit lower bound for the smallest eigenvalue of its normalised adjacency operator, which depends on the graph only through its degree and its vertex-Cheeger constant. We also prove an analogous result for a large class of irregular graphs, obtained as spanning subgraphs of vertex-transitive graphs. Using a result of Babai, we obtain a lower bound for the smallest eigenvalue of the normalised adjacency operator of a vertex-transitive graph in terms of its diameter and its degree.

Revised:

Accepted:

Published online:

Keywords: Spectral gap, diameter, vertex-transitive graphs, discrete Cheeger–Buser inequality

Biswas, Arindam ^{1};
Saha, Jyoti Prakash ^{2}

@article{ALCO_2023__6_3_689_0, author = {Biswas, Arindam and Saha, Jyoti Prakash}, title = {A spectral bound for vertex-transitive graphs and their spanning subgraphs}, journal = {Algebraic Combinatorics}, pages = {689--706}, publisher = {The Combinatorics Consortium}, volume = {6}, number = {3}, year = {2023}, doi = {10.5802/alco.278}, language = {en}, url = {https://alco.centre-mersenne.org/articles/10.5802/alco.278/} }

TY - JOUR AU - Biswas, Arindam AU - Saha, Jyoti Prakash TI - A spectral bound for vertex-transitive graphs and their spanning subgraphs JO - Algebraic Combinatorics PY - 2023 SP - 689 EP - 706 VL - 6 IS - 3 PB - The Combinatorics Consortium UR - https://alco.centre-mersenne.org/articles/10.5802/alco.278/ DO - 10.5802/alco.278 LA - en ID - ALCO_2023__6_3_689_0 ER -

%0 Journal Article %A Biswas, Arindam %A Saha, Jyoti Prakash %T A spectral bound for vertex-transitive graphs and their spanning subgraphs %J Algebraic Combinatorics %D 2023 %P 689-706 %V 6 %N 3 %I The Combinatorics Consortium %U https://alco.centre-mersenne.org/articles/10.5802/alco.278/ %R 10.5802/alco.278 %G en %F ALCO_2023__6_3_689_0

Biswas, Arindam; Saha, Jyoti Prakash. A spectral bound for vertex-transitive graphs and their spanning subgraphs. Algebraic Combinatorics, Volume 6 (2023) no. 3, pp. 689-706. doi : 10.5802/alco.278. https://alco.centre-mersenne.org/articles/10.5802/alco.278/

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