Some Properties of Von Neumann Regular Graphs of Rings

Diamond Kharkongor (North-Eastern Hill University Shillong-22, Meghalaya, India)
Laithun Boro (North-Eastern Hill University Shillong-22, Meghalaya, India)
Madan Mohan Singh (North-Eastern Hill University Shillong-22, Meghalaya, India)
Sanghita Dutta (North-Eastern Hill University Shillong-22, Meghalaya, India)

Journal of the Indonesian Mathematical Society
VOLUME 28 NUMBER 2 (JULY 2022)

Let R be a ring with unity. Taloukolaei and Sahebi [2] introduced the Von Neumann regular graph GV nr+(R) of a ring, whose vertex set is R and two distinct vertices x and y are adjacent if and only if x + y is a Von Neumann regular element. In this article, we investigate some new properties of GV nr+(R) such as traversability, pancyclic, unicyclic, chordal and perfect. We also investigate the domination parameters of GV nr+(R) such as dominating set, domination number, total domination number, connected domination number and give the condition when the GV nr+(R) is an excellent graph. Finally we determine the bondage number.