Topological indices are numerical parameters of a molecular graph G which characterize its topology. On the other hands, computing the connectivity indices of molecular graphs is an important branch in chemical graph theory. Therefore, we compute First Zagreb index Zg   <span style="font-family: TimesNewRomanPS-Italic...

let $g $ be a finite group and let $gamma(g)$ be the prime graph‎ ‎of g‎. ‎assume $2 < q = p^{alpha} < 100$‎. ‎we determine finite groups‎ ‎g such that $gamma(g) = gamma(u_3(q))$ and prove that if $q neq‎ ‎3‎, ‎5‎, ‎9‎, ‎17$‎, ‎then $u_3(q)$ is quasirecognizable by prime graph‎, ‎i.e‎. ‎if $g$ is a finite group with the same prime graph as the‎ ‎finite simple group $u_3(q)$‎, ‎then $g$ has a un...

From its early beginnings up to nowadays, algebraic number theory has evolved in symbiosis with Galois theory: indeed, one could hold that it consists in the very study of the absolute Galois group of the field of rational numbers. Nothing like that can be said of transcendental number theory. Nevertheless, couldn’t one associate conjugates and a Galois group to transcendental numbers such as π...

A central theme in distributed network algorithms concerns understanding and coping with the issue of locality. Despite considerable progress, research efforts in this direction have not yet resulted in a solid basis in the form of a fundamental computational complexity theory for locality. Inspired by sequential complexity theory, we focus on a complexity theory for distributed decision proble...

We consider pairs of automorphisms $(\phi,\sigma)$ acting on fields Laurent or Puiseux series: shift operators $(\phi\colon x\mapsto x+h\_1, \sigma\colon x+h\_2)$, $q$-difference q\_1x$, $\sigma\colon q\_2x)$, and Mahler x^{p\_1},\ x^{p\_2})$. Given a solution $f$ to linear $\phi$-equation $g$ an algebraic $\sigma$-equation, both transcendental, we show that are algebraically independent over t...