Haneen Kareem Hussein Al-janabi Some Algebraic Aspects of Graphs c. PhD-dolgozatának házi védésére 2022. augusztus 23-án 14.00-tól kerül sor a H306-os teremben.

Témavezető: Bacsó Gábor (SZTAKI), belső konzulens: Wettl Ferenc. Bírálók: Dr Szigeti Jenő (Miskolci Egyetem), Bozóki Sándor PhD (Budapesti Corvinus Egyetem).

A dolgozat kivonata: The main topics of this work are the chromatic polynomials and the zero-divisor graphs of rings.

A polynomial $p(\lambda)$ is called an integral-root polynomial if all of its roots are integers. A graph $G$ is an integral-root graph if $P(G,\lambda)$ is an integral-root polynomial. Here we solve the uniqueness problem for such graphs. We determine the chromatic polynomial and study the chromatic uniqueness of certain line graphs. Furthermore, we discuss the following question: For which numbers $n$ is the zero-divisor graph $\Pi(Z_n)$ $\chi$-unique? For an odd square-free non-prime $n$, the problem is open, but we give the answer for every other case.