On linear algebra of balance-binomial graphs

On the spectra of generalized Fibonomial and Jacobsthal-binomial graphs

“…Thus, if we talk about the spectra of the generalized Fibonomial graphs, there are four kinds of the adjacency spectrum according to the p and q . Adjacency spectrum of the Fibonomial graphs and balance-binomial graphs are given in [1] and [4,9], respectively. Clearly J n has eigenvalues 0 n−1 , n and 0 n has eigenvalues 0 n .…”

“…Spectral properties and energy of Fibonomial graphs were investigated in the same paper. Next, balance-binomial graphs were introduced in [9] whose entries are dependent on the balancing numbers. Balance-binomial coefficents were used instead of Fibonomial coefficents in [9].…”

“…Next, balance-binomial graphs were introduced in [9] whose entries are dependent on the balancing numbers. Balance-binomial coefficents were used instead of Fibonomial coefficents in [9]. However, actually, balance-binomial graphs are exactly the same with binomial graphs.…”

“…However, actually, balance-binomial graphs are exactly the same with binomial graphs. This could be easily seen by comparing [4] and [9]. By the motivation of these results, in this work, we first examine the situation for the generalized Fibonacci numbers and so define the generalized Fibonomial graphs with a more general perspective.…”