On some applications related with algebraic structures through different well known graphs

Abstract

Lot of achievements have been done to comprehend the latest phenomena of our life by discussing the interrelationship of two boughs, graph theory and algebra, of mathematics. In the modern time, it seems to be of great importance to study about eminent, extensive and certifiable applications through well known tools of graph theory. Combinatorial commutative algebra, moderately new, quickly creating numerical tool and foremost tendril of mathematics, has been used exhaustively to solve a list of open problems in algebra under the shadow of graphs. It can be helpful, instead of algebraically, to find the metric dimension of zero-divisor graphs, NP-complete problem, related with finite mathematical structures. In this article we shall discuss some graphs, zero-divisor graphs of finite Boolean rings and balanced bipartite graphs of conjugacy closed loops, and their associated applications.

Subject Classification: (2010):

• 05Exx
• 05C25
• 05E40

Keywords:

• Metric dimension
• Zero-divisor graph
• Conjugacy closed loop
• Balanced bipartite graph