Let’s walk through the argument using the following triangle-free graph as an example. Start by picking any vertex in the graph and considering all of its neighbors — the vertices connected to it by ...

Just to correct some terminology, a loop is an edge from a vertex to itself ... edges in the graph) many paths between two vertices (even in simple graphs). For example, consider graphs like ...

the vertex is a maximum turning point We can identify these properties from a quadratics graph or equation.