Simplicial vertex (graph theory)

A simplicial vertex is a graph vertex whose graph neighbourhood is a clique. Every isolated vertex and every leaf of a graph qualifies. In the three-triangle chordal graph, initially $a,e$ qualify, but $b$ only becomes a simplicial vertex after deleting $a$. This is a property of adjacency in a graph; a vertex of a simplicial complex is an element of a different kind of structure.