Generalized distance spectral radius of some t-partitioned transmission regular graphs

Let [Formula: see text] be an [Formula: see text]-vertex connected graph with the distance matrix [Formula: see text] and the diagonal matrix of transmissions [Formula: see text]. The generalized distance matrix of a connected graph [Formula: see text] is [Formula: see text], where [Formula: see text], [Formula: see text]. Through this matrix one can study distance, distance Laplacian, distance signless Laplacian, and [Formula: see text]- spectra of [Formula: see text] in a unified way. A simple connected graph [Formula: see text] is called [Formula: see text]-partitioned transmission regular if the vertex set of [Formula: see text] can be partitioned as [Formula: see text] such that for any pair of indices [Formula: see text] (not necessarily distinct) in [Formula: see text] and [Formula: see text], [Formula: see text] is constant. In this paper, for the spider graph [Formula: see text] and the radar graph [Formula: see text], we find matrices of order [Formula: see text] (quotient matrices) corresponding to [Formula: see text] and [Formula: see text] such that the largest eigenvalues of these matrices are generalized distance spectral radius of [Formula: see text] and [Formula: see text], respectively. Moreover, we determine the full [Formula: see text]-spectrum of [Formula: see text] and [Formula: see text] (wheel graph).