Graphs & Digraphs

1-factor 2-cell embedding a₁ acyclic adjacency matrix arcs Assume B₁ bipartite graph block chromatic number complete graph component of G connected graph contradiction Corollary cubic graph cut-vertex cycle of G D₁ defined denote Determine digraph disconnected distinct vertices edge of G edge-reconstructible eigenvalues embedding of G eulerian eulerian circuit exists F₂ follows G contains G is connected G of order G₁ G₂ genus graph G graph of order H₁ hamiltonian cycle hamiltonian graphs hamiltonian path Hence homeomorphic hypothesis implies incident induced subgraph internally disjoint isolated vertices isomorphic K₁ Let G line graph maximum Menger's Theorem minimum number n-connected nonempty graph number of vertices orbits P₁ partition permutation Petersen graph planar graph plane positive integer Prove result subgraph H subgraph of G subset Suppose tournament trail triangulation u-v path u₁ upper embeddable v₁ vertex set vertices of G w₁ w₂