No abstract

In this study, we introduce a new graph family. Then, we calculate eigenvalues of the adjacency and the Laplacian matrix of this graph family. Moreover, we show that the perfect matching number of this graph family equals to special second order recurrence by hafnian method. For some special kinds of this family, we obtain that the perfect matching number of corresponding graphs equals to some famous number sequences such as Fibonacci, Pell and Jacobsthal numbers. Also, we find energies and obtain upper bounds for Laplacian energies of these graphs.

This note provides formula for determinant and inverse of r-circulant matrices with general sequences of third order. In other words, the study combines many papers in the literature.AMS2010: 15A09; 15A15.

Abstract:Recently, determinant computation of circulant type matrices with well-known number sequences has been studied, extensively. This study provides the determinants of the RFMLR, RLMFL, RFPrLrR and RLPrFrL circulant matrices with generalized number sequences of second order.