Let G be a finite group and let $GK(G)$ be the prime graph of G. We assume that $n$ is an odd number. In this paper, we show that if $GK(G)=GK(B_n(p))$, where $ngeq 9$ and $pin {3,5,7}$, then G has a unique nonabelian composition factor isomorphic to $B_n(p)$ or $C_n(p)$ . As consequences of our result, $B_n(p)$ is quasirecognizable by its spectrum and also by a new proof, the ...

For two graphs $mathrm{G}$ and $mathrm{H}$ with $n$ and $m$ vertices, the corona $mathrm{G}circmathrm{H}$ of $mathrm{G}$ and $mathrm{H}$ is the graph obtained by taking one copy of $mathrm{G}$ and $n$ copies of $mathrm{H}$ and then joining the $i^{th}$ vertex of $mathrm{G}$ to every vertex in the $i^{th}$ copy of $mathrm{H}$. The neighborhood corona $mathrm{G}starmathrm{H}$ of $mathrm{G}$ and $...

the robust coloring problem (rcp) is a generalization of the well-known graph coloring problem where we seek for a solution that remains valid when extra edges are added. the rcp is used in scheduling of events with possible last-minute changes and study frequency assignments of the electromagnetic spectrum. this problem has been proved as np-hard and in instances larger than 30 vertices, meta-...