$$G$$ is a graph on $$n$$ vertices and $$2n-2$$ edges. The edges of $$G$$ can be partitioned into two edge-disjoint spanning trees. Which of the following in NOT true for $$G$$?

Which of the following graphs has an Eulerian circuit?

Let Graph$$(x)$$ be a predicate which denotes that $$x$$ is a graph. Let Connected$$(x)$$ be a predicate which denotes that $$x$$ is connected. Which of the following first order logic sentences DOES NOT represent the statement: $$Not\,\,\,every\,\,\,graph\,\,\,is\,\,\,connected?$$

Consider the undirected graph $$G$$ defined as follows. The vertices of $$G$$ are bit strings of length $$n$$. We have an edge between vertex $$u$$ and vertex $$v$$ if and only if $$u$$ and $$v$$ differ in exactly one bit position (in other words, $$v$$ can be obtained from $$u$$ by flipping a single bit). The ratio of the choromatic number of $$G$$ to the diameter of $$G$$ is