Abstract
To gain better understanding of molecules, social nods, urban planning and other networks, we need to represent them as graphs which is why graph theory is a very active area in mathematics. In addition, it is well known that the Fibonacci sequence appears in many different areas. Recently, the Fibonacci and Lucas graphs were introduced and some of their algebraic properties were established. In this work, we consider generalized Lucas graphs and establish some algebraic properties. Studying the generalized Lucas graphs yields a wider class of graphs since the Fibonacci and Lucas graphs are special cases of the generalized Lucas graphs.