A set of edges $$X\subseteq E(G)$$X⊆E(G) of a graphGis an edge general position set if no three edges fromXlie on a common shortest path inG. The cardinality of a largest edge general position set ofGis the edge general position number ofG. In this paper, edge general position sets are investigated in partial cubes. In particular, it is proved that the union of two largest $$\Theta $$Θ -classes of a Fibonacci cube or a Lucas cube is a maximal edge general position set.

In this paper, we consider a generalization of Horadam sequence $\{ w_{n} \} ${wn} which is defined by the recurrence relation $w_{n}=\chi ( n ) w_{n-1}+cw_{n-2}$wn=χ(n)wn−1+cwn−2 , where $\chi ( n ) =a$χ(n)=a if n is even, $\chi ( n ) =b$χ(n)=b if n is odd with arbitrary initial conditions $w_{0}$w0 , $w_{1}$w1 and nonzero real numbers a, b and c. As a special case, by taking the initial conditions 0, 1 and 2, b we define the sequences $\{ u_{n} \} ${un} and $\{ v_{n} \} ${vn} , respectively. The main purpose of this study is to derive some basic properties of the sequences $\{ u _{n} \} ${un} , $\{ v_{n} \} ${vn} and $\{ w_{n} \} ${wn} by using a matrix approach.

In this paper, we present a new class of Leonardo hybrid numbers that incorporate quantum integers into their components. This advancement presents a broader generalization of the q-Leonardo hybrid numbers. We explore some fundamental properties associated with these numbers. Moreover, we study special Leonardo quaternions over finite fields. In particular, we determine the Leonardo quaternions that are zero divisors or invertible elements in the quaternion algebra over the finite field ${\mathbb{Z}}_p$ for special values of prime integer p.