Problems

For 0<α≤ 1 , among all trees, characterize the tree which has the maximum generalized distance spectral radius.

The characteristic set of a path-star tree contains an edge.

We have max_t m_H_t(2, ∞) = max_t m_G_t(2, ∞) and max_t m_H_t(-∞, -2) = max_t m_G_t(-∞, -2).

For k,n,α ∈N , let G ∈ G_n,α have the minimum spectral radius in G_n,α . Then for sufficiently large n, (1) G ≅ F(k,k,k+1) for α=3,n=3k+1, (2) G ≅ F(k+1,k,k+1) for α=3 and n=3k+2, (3) G ≅ F(k,k,k,k+1) for α=4 and n=4k+1, (4) G ≅…

For any graph G on n ≥ 4 vertices, ▷ ∂{2}^{L}(G)≥n with equality if and only if G is the complete graph K{n} or K_{n} minus an edge; ▷ if n ≠7, then ∂{2}^{L}(G)≤∂{2}^{L}(P_{n}) with equality if and only if G is the path P_{n} ; ▷ if G is a…

Determination of ξ_G(λ_χ) for general chromatic characteristic polynomials of all 2-regular bipartite graphs is still in progress.

Suppose that the graphs Γ_1 and Γ_2 have the same refined spectra. Are their complements cospectral?

No two non-isomorphic H-shape trees are L-cospectral.

Let S be the parameter matrix of a k-transversal in a d-uniform r-regular hyper graph G. Then the characteristic polynomial of S is φ(λ)=λ^d-2∏_i=j^d(λ-ξ^jkr), where ξ is a d-th primitive root of unity.