In this paper, we derive a more precise version of the Strong Pair Correlation Conjecture on the zeros of the Riemann zeta function under Riemann Hypothesis and Twin Prime Conjecture.

We consider the Zassenhaus conjecture for the normalized unit group of the integral group ring of the Mathieu sporadic group M 12. As a consequence, we confirm for this group the Kimmerle's conjecture on prime graphs.

Let $G$ be a group. The order graph of $G$ is the (undirected)graph $Gamma(G)$,those whose vertices are non-trivial subgroups of $G$ and two distinctvertices $H$ and $K$ are adjacent if and only if either$o(H)|o(K)$ or $o(K)|o(H)$. In this paper, we investigate theinterplay between the group-theoretic properties of $G$ and thegraph-theoretic properties of $Gamma(G)$. For a finite group$G$, we s...

We investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the simple Janko group J1. As a consequence, for this group we confirm Kimmerle’s conjecture on prime graphs.

We consider the Zassenhaus conjecture for the normalized unit group of the integral group ring of the McLaughlin sporadic group McL. As a consequence, we confirm for this group the Kimmerle’s conjecture on prime graphs.

We show that if G is a connected bridgeless cubic graph whose every 2-factor is comprised of cycles of length five then G is the Petersen graph. ”The Petersen graph is an obstruction to many properties in graph theory, and often is, or conjectured to be, the only obstruction”. This phrase is taken from one of the series of papers by Robertson, Sanders, Seymour and Thomas that is devoted to the ...

The minimum rank of a graph has been an interesting and well studied parameter 6 investigated by many researchers over the past decade or so. One of the many unresolved questions on 7 this topic is the so-called graph complement conjecture, which grew out of a workshop in 2006. This 8 conjecture asks for an upper bound on the sum of the minimum rank of a graph and the minimum rank 9 of its comp...