I'm having a bit of a trouble with the below question Given G is an undirected graph, the degree of a vertex v, denoted by deg(v), in graph G is the number of neighbors of v. Prove that the …

Usually one speaks of adjacent vertices, but of incident edges. Two vertices are called adjacent if they are connected by an edge. Two edges are called incident, if they share a vertex. Also, a …

Dec 6, 2025 · The least number of vertices that a polyhedron can have, such that its diagonal faces enclose an interior solid region? Note: "interior" means the solid does not intersect the …

Dec 27, 2025 · The above construction provides an explicit example of a $6$ -regular graph on $19$ vertices that is locally a $ (3,3)$ -windmill. If one wishes to analyze the graph by hand …

Oct 23, 2022 · I would approach the issue from a completely different direction. Consider a triangle in 3D with vertices at $\vec {v}_0$, $\vec {v}_1$, and $\vec {v}_2$. It has a directed …

Dec 11, 2010 · Anyone know of an online tool available for making graphs (as in graph theory - consisting of edges and vertices)? I have about 36 vertices and even more edges that I wish to …

Let G G be a k k -connected graph. Meaning, G G has no fewer than k k vertices, and for every set of k − 1 k 1 or fewer vertices, if we remove them from G G, the graph stays connected (Of …

13 Problem Find the cut vertices and cut edges for the following graphs My understanding of the definitions: A cut vertex is a vertex that when removed (with its boundary edges) from a graph …

Is a set of vertices all isolated included? (some solutions say yes, but how can it then be called 'directed?') The n -vertex null digraph (i.e. n vertices and no edges) is consistently regarded as …

Mar 19, 2021 · Here are a couple hints. I will consider the vertices to be length- n n bitstrings. An edge connects two vertices if the vertices differ by a single bit flip. How many edges are …