**Speaker:** Farzaneh Gholaminezhad (Halle)

**Title:** *The G-Graphs and the Hamiltonian Cayley Graphs*

**Abstract:**

For a finite group \(G\) and a non empty subset of generators \(S \subseteq G\), \(\phi(G,S)=(V,E)\) is a \(G\)-graph where \(V\) is the union of the sets of \((x, sx, s^2 x, ... , s^{o(s)-1}x)\) for all \(s \in S\). Two distinct vertices \((s)x\) and \((t)y\) are adjacent iff \(|<s>x \cap <t>y | \geq 1\).

Bretto et. al defined the \(G\)-graph in 2005 in order to answer some conjectures in graph theory like graph isomorphism and cage problem. Here I will present my results on Lovasz' conjecture (1970) and find the Hamiltonian Cayley graphs.