Eigenvalues of Cayley graphs
arXiv:1809.09829 · doi:10.37236/8569
Abstract
We survey some of the known results on eigenvalues of Cayley graphs and their applications, together with related results on eigenvalues of Cayley digraphs and generalizations of Cayley graphs.
arXiv commentThe final version
References in corpus (36)
- Perfect state transfer in quantum spin networks
- Perfect Transfer of Arbitrary States in Quantum Spin Networks
- A Review of Perfect State Transfer and its Application as a Constructive Tool
- Distance-regular graphs
- Quantum Networks on Cubelike Graphs
- Perfect state transfer in cubelike graphs
- Perfect state transfer on distance-regular graphs and association schemes
- Almost perfect state transfer in quantum spin chains
- Unsolved Problems in Group Theory. The Kourovka Notebook
- On the eigenvalues of Cayley graphs on the symmetric group generated by a complete multipartite set of transpositions
- The spectral gap of the ferromagnetic XXZ chain
- Groups all of whose undirected Cayley graphs are integral
- Integral circulant graphs of prime power order with maximal energy
- The maximal energy of classes of integral circulant graphs
- New bounds for the max--cut and chromatic number of a graph
- Quadratic unitary Cayley graphs of finite commutative rings
- The second largest eigenvalues of some Cayley graphs on alternating groups
- Quasirandom Cayley graphs
- Circulant Digraphs Integral over Number Fields
- Integral equienergetic non-isospectral unitary Cayley graphs
- A note on a Cayley graph of S_n
- Longest Induced Cycles on Cayley Graphs
- Cayley-type graphs for group-subgroup pairs
- Rationality conditions for the eigenvalues of normal finite Cayley graphs
- -eigenfunctions of the Star graphs
- Aldous' spectral gap property for normal Cayley graphs on symmetric groups
- Ramanujan circulant graphs and the conjecture of Hardy-Littlewood and Bateman-Horn
- Spectral properties of generalized Paley graphs and their associated irreducible cyclic codes
- Cayley sum graphs and eigenvalues of -fullerenes
- Simple eigenvalues of cubic vertex-transitive graphs
- Group representations that resist random sampling
- Spectral and Combinatorial Properties of Some Algebraically Defined Graphs
- On the flip graphs on perfect matchings of complete graphs and signed reversal graphs
- A note on the relation between two properties of random graphs
- On expander Cayley graphs from Galois rings
- The second eigenvalue of some normal Cayley graphs of high transitive groups
Cited by in corpus (10)
- Integral equienergetic non-isospectral unitary Cayley graphs
- Quantum symmetries of Cayley graphs of abelian groups
- Aldous' spectral gap property for normal Cayley graphs on symmetric groups
- The second largest eigenvalue of normal Cayley graphs on symmetric groups generated by cycles
- Singular Graphs with Dihedral Group Action
- Universality classes for purification in nonunitary quantum processes
- On expander Cayley graphs from Galois rings
- Intersective sets over abelian groups
- The second largest eigenvalue of some nonnormal Cayley graphs on symmetric groups
- On the second eigenvalue of a Cayley graph of the symmetric group