Search Results for ""

A rooted graph is a graph in which one node is labeled in a special way so as to distinguish it from other nodes. The special node is called the root of the graph. The rooted ...

The nth-order Sierpiński tetrahedron graph is the connectivity graph of black triangles in the nth iteration of the tetrix fractal. The first three iterations are shown ...

A graph G is said to be disconnected if it is not connected, i.e., if there exist two nodes in G such that no path in G has those nodes as endpoints. The numbers of ...

A simple unlabeled graph on n vertices is called pancyclic if it contains cycles of all lengths, 3, 4, ..., n. Since a pancyclic graph must contain a cycle of length n, ...

A fundamental structural result in extremal graph theory due to Szemerédi (1978). The regularity lemma essentially says that every graph can be well-approximated by the union ...

Let m(G) be the cycle rank of a graph G, m^*(G) be the cocycle rank, and the relative complement G-H of a subgraph H of G be defined as that subgraph obtained by deleting the ...

A uniquely pancyclic graph is a graph that has exactly one cycle of each length between 3 and the graph's vertex count. Uniquely pancyclic graphs are therefore a special case ...

Let G be a k-regular graph with girth 5 and graph diameter 2. (Such a graph is a Moore graph). Then, k=2, 3, 7, or 57. A proof of this theorem is difficult (Hoffman and ...

A graph is called cordial if it is possible to label its vertices with 0s and 1s so that when the edges are labeled with the difference of the labels at their endpoints, the ...

Graphs corresponding to closed walks of length k are known as k-cyclic graphs, or C_k-graphs for short. C_k-graphs are connected by definition. The numbers of C_k-graphs for ...