Which one of the following in NOT necessarily a property of Group?

consider the binary relation $$R = \left\{ {\left( {x,y} \right),\,\left( {x,z} \right),\,\left( {z,x} \right),\,\left( {z,y} \right)} \right\}$$ on the set $$\left\{ {x,\,y,\,z} \right\}$$. which one of the following is TRUE?

What is the chromatic number of an $$n$$-vertex simple connected graph which does not contain any odd length cycle? Assume $$n \ge 2$$.

Which one of the following is TRUE for any simple connected undirected graph with more than $$2$$ vertices?