Question
Let $G$ be a simple graph. Show that the relation $R$ on the set of vertices of $G$ such that $u R v$ if and only if there is an edge associated to $\{u, v\}$ is a symmetric, irreflexive relation on $G$.
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Let $G$ be an undirected graph with a loop at every vertex. Show that the relation $R$ on the set of vertices of $G$ such that $u R v$ if and only if there is an edge associated to $\{u, v\}$ is a symmetric, reflexive relation on $G .$
Graphs
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Show that the graph G is its own converse if and only if the relation associated with G (see Section 9.3) is symmetric.
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