الرسوم البيانية المرتبطة بالزمر التبديلية المنتهية

Abstract

Let 𝐴 be a finite abelian group, An undirected graph 𝐺(𝐴) of a finite group 𝐴 is introduced and defined as an undirected simple graph whose vertex set is 𝑉(G) and two distinct vertices 𝑢 and 𝑣 are adjacent if and only if 𝑢2 ≠ 𝑣2. In this paper, for a finite group 𝐴 = (ℤ𝑛, . ), the degrees of vertices, the number of edges of 𝐺(𝐴), the eccentricity, diameter, girth, chromatic number are computed. Furthermore, Hamiltonian and Eulerian cycles of 𝐺 are proposed.