Matching Number, Independence Number, and Covering Vertex Number of Γ(Zn)

• Main Authors: Eman AbuHijleh, Mohammad Abudayah, Omar Alomari, Hasan Al-Ezeh
• Format: Article
• Language: English
• Published: MDPI AG 2019-01-01
• Series: Mathematics
• Subjects: zero-divisor graphs; matching number; independence number; and vertex covering number
• Online Access: http://www.mdpi.com/2227-7390/7/1/49

Graph invariants are the properties of graphs that do not change under graph isomorphisms, the independent set decision problem, vertex covering problem, and matching number problem are known to be NP-Hard, and hence it is not believed that there are efficient algorithms for solving them. In this paper, the graph invariants matching number, vertex covering number, and independence number for the zero-divisor graph over the rings Z p k and Z p k q r are determined in terms of the sets S p i and S p i q j respectively. Accordingly, a formula in terms of p , q , k , and r, with n = p k , n = p k q r is provided.