D-Integral, $$D^Q$$ -Integral and $$D^L$$ -Integral Generalized Double-Wheel Graphs

Abstract

The graph \(aK_{m,m}\nabla C_{n}\) is named the generalized double-wheel graph. A graph G is said to be M-integral (resp. A-integral, D-integral, \(D^L\)-integral or \(D^Q\)-integral) if all eigenvalues of its matrix M (resp. adjacency matrix A(G) , distance matrix D(G) , distance Laplacian matrix \(D^L(G)\) or distance signless Laplacian matrix \(D^Q(G)\)) are integers. In this paper, we completely determine all D-integral, \(D^L\)-integral and \(D^Q\)-integral generalized double-wheel graphs respectively.