In the last couple of decades, there has been a big upsurge of research on graphs defined
on algebraic structures (groups, rings, vector spaces, semigroups, and others). Much of this …

In an earlier paper, the authors considered three types of graphs, and three equivalence
relations, defined on a group, viz.\the power graph, enhanced power graph, and commuting …

In this work, we introduce a new concept called the tripotent divisor graph of a commutative
ring. It is defined with vertices set in a ring R, where distinct vertices r1 and r2 are connected …

We associate a sequence of positive integers, termed the type sequence, with a cochordal
graph. Using this type sequence, we compute all graded Betti numbers of its edge ideal. We …

For an element x of a commutative ring R, let \Gamma_x(R) be the graph whose vertices are
the elements of R that divide x such that distinct vertices r and s are adjacent if and only if …