26 research outputs found
Triangle-degree and triangle-distinct graphs
Let be a simple graph and be a vertex of . The triangle-degree of
in is the number of triangles that contain . While every graph has
at least two vertices with the same degree, there are graphs in which every
vertex has a distinct triangle-degree. In this paper, we construct an infinite
family of graphs with this property. We also study the vertex degrees and size
of graphs with this property