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Diamond graph
In the mathematical field of graph theory, the diamond graph is a planar undirected graph with 4 vertices and 5 edges.〔ISGCI: Information System on Graph Classes and their Inclusions "(List of Small Graphs )".〕 It consists of a complete graph minus one edge.
The diamond graph has radius 1, diameter 2, girth 3, chromatic number 3 and chromatic index 3. It is also a 2-vertex-connected and a 2-edge-connected graceful〔Sin-Min Lee, Y.C. Pan and Ming-Chen Tsai. "On Vertex-graceful (p,p+l)-Graphs". ()〕 Hamiltonian graph.
==Diamond-free graphs and forbidden minor==
A graph is diamond-free if it has no diamond as an induced subgraph. The triangle-free graphs are diamond-free graphs, since every diamond contains a triangle.
The family of graphs in which each connected component is a cactus graph is downwardly closed under graph minor operations. This graph family may be characterized by a single forbidden minor. This minor is the diamond graph.〔.〕
If both the butterfly graph and the diamond graph are forbidden minors, the family of graphs obtained is the family of pseudoforests.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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