Problem $1.$ Consider $G=(V,E)$ for figure $1$ where $V$ is the vertex$/$nodes and $E$ is the edges. $($Hint: for

example, for $V=\{a,b\}$ and the edge would be $E=\{e_{ab}\}.)$

$(1)$ Write down set of $V$ and $E.$

$(2)$ Is $G$ a complete graph? Explain your reason.

$(3)$ Is $G$ a tree? Explain your reason.

$(4)$ Write down the degree for node a and $c.$