The metric dimension & distance spectrum of non-commuting graph of dihedral group

The non-commuting graph [Formula: see text] of a finite group [Formula: see text] has vertex set as [Formula: see text] and any two vertices [Formula: see text] are adjacent if [Formula: see text]. In this paper, we have determined the metric dimension and resolving polynomial of [Formula: see text], where [Formula: see text] is the dihedral group of order [Formula: see text]. The distance spectrum of [Formula: see text] has also been determined for all [Formula: see text].

Non-uniform sampling in pulse dipolar spectroscopy by EPR: the redistribution of noise and the optimization of data acquisition

Non-uniform schemes for collection of pulse dipole spectroscopy data can decrease and redistribute noise in the distance spectrum for increased sensitivity and throughput.

The Generalized Distance Spectrum of the Join of Graphs

Let G be a simple connected graph. In this paper, we study the spectral properties of the generalized distance matrix of graphs, the convex combination of the symmetric distance matrix D ( G ) and diagonal matrix of the vertex transmissions T r ( G ) . We determine the spectrum of the join of two graphs and of the join of a regular graph with another graph, which is the union of two different regular graphs. Moreover, thanks to the symmetry of the matrices involved, we study the generalized distance spectrum of the graphs obtained by generalization of the join graph operation through their eigenvalues of adjacency matrices and some auxiliary matrices.