Sophomore at PEC, India.Pursuing Bachelor's in Computer Science and Engineering.Mathematics EnthusiastGood grasp on C++, Python and Javascript and programming in general.Always eager to learn and apply.
Find the strongly connected components of each of these graphs. Graph cannot copy
Let $G=(V, E)$ be a simple graph. Let $R$ be the relation on $V$ consisting of pairs of vertices $(u, v)$ such that there is a path from $u$ to $v$ or such that $u=v .$ Show that $R$ is an equivalence relation.
Suppose that $v$ is an endpoint of a cut edge. Prove that $v$ is a cut vertex if and only if this vertex is not pendant.
Show that a simple graph with at least two vertices has at least two vertices that are not cut vertices.
A vertex basis in a directed graph $G$ is a minimal set $B$ of vertices of $G$ such that for each vertex $v$ of $G$ not in $B$ there is a path to $v$ from some vertex $B$ .What is the significance of a vertex basis in an influence graph (described in Example 2 of Section 10.1$) ?$ Find a vertex basis in the influence graph in that example.
How many nonisomorphic connected simple graphs are there with $n$ vertices when $n$ is$\begin{array}{llll}{\text { a) } 2 ?} & {\text { b) } 3 ?} & {\text { c) } 4 ?} & {\text { d) } 5 ?}\end{array}$
