Let $R$ be an associative ring with identity and $Z^*(R)$ be its set of non-zero zero divisors.  The zero-divisor graph of $R$, denoted by $Gamma(R)$, is the graph whose vertices are the non-zero  zero-divisors of  $R$, and two distinct vertices $r$ and $s$ are adjacent if and only if $rs=0$ or $sr=0$.  In this paper, we bring some results about undirected zero-divisor graph of a monoid ring o...

Good tracking requires significant quintessence energy fraction, even in the past, but a potential energy that is not yet truly slow-rolling. The supernova bound on cosmic acceleration excludes constant equation of state and inverse power potentials, but allows the SUGRA potential and other good trackers, in which quintessence energy domination and kinetic energy suppression both began only rec...

Let N be a near-ring. In this paper, we associate a graph corresponding to the 3-prime radical I of N , denoted by ΓI(N). Further we obtain certain topological properties of Spec(N), the spectrum of 3-prime ideals of N and graph theoretic properties of ΓI(N). Using these properties, we discuss dominating sets and connected dominating sets of ΓI(N).