Special number sequences play important role in many areas of science. One of them named as Fibonacci sequence dates back to 820 years ago. There is a lot of research on Fibonacci numbers due to their relation with the golden ratio and also due to many applications in Chemistry, Physics, Biology, Anthropology, Social Sciences, Architecture, Anatomy, Finance, etc. A slight variant of the Fibonacci sequence was obtained in the eighteenth century by Lucas and therefore named as Lucas sequence. There are very natural close relations between graph theory and other areas of Mathematics including number theory. Recently Fibonacci graphs have been introduced as graphs having consecutive Fibonacci numbers as vertex degrees. In that paper, graph theory was connected with number theory by means of a new graph invariant called \(\varOmega (D)\) for a realizable degree sequence D defined recently. \(\varOmega (D)\) gives information on the realizability, number of components, chords, loops, pendant edges, faces, bridges, connectedness, cyclicness, etc. of the realizations of D and is shown to have several applications in graph theory. In this paper, we define Lucas graphs as graphs having degree sequence consisting of n consecutive Lucas numbers and by using \(\varOmega \) and its properties, we obtain a characterization of these graphs. We state the necessary and sufficient conditions for the realizability of a given set D consisting of n successive Lucas numbers for every n and also list all possible realizations called Lucas graphs for \(1 \le n \le 4\) and afterwards give the general result for \(n \ge 5\).

特殊的数字序列在许多科学领域中都起着重要作用。其中一个名为斐波那契数列的历史可以追溯到820年前。由于斐波那契数与黄金比率有关，并且在化学，物理，生物学，人类学，社会科学，建筑，解剖学，金融等领域有许多应用，因此对斐波那契数进行了大量研究。由卢卡斯（Lucas）在18世纪获得，因此被称为卢卡斯（Lucas）序列。图论与包括数论在内的其他数学领域之间有着非常自然的密切关系。最近，斐波那契图被引入为具有连续斐波那契数作为顶点度的图。在那篇论文中，图论与数论通过一个称为\（\ varOmega（D）\）用于最近定义的可实现的度数序列D。\（\ varOmega（d）\）给出了关于可实现信息，组件，和弦，环路，挂件边，面，桥梁，连通，cyclicness，的实现中的数目等d和被示出为具有在图若干应用理论。在本文中，我们将卢卡斯图定义为具有由n个连续卢卡斯数组成的度序的图，并通过使用\（\ varOmega \）及其性质来获得这些图的特征。我们陈述了由n构成的给定集合D的可实现性的充要条件每n个连续的Lucas数，并列出\（1 \ le n \ le 4 \）的所有可能的实现，称为Lucas图，然后给出\（n \ ge 5 \）的一般结果。