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In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency. A regular directed graph must also satisfy the stronger condition that the indegree and outdegree of each vertex are equal to each other.〔 〕 A regular graph with vertices of degree k is called a k‑regular graph or regular graph of degree k. Regular graphs of degree at most 2 are easy to classify: A 0-regular graph consists of disconnected vertices, a 1-regular graph consists of disconnected edges, and a 2-regular graph consists of disconnected cycles and infinite chains. A 3-regular graph is known as a cubic graph. A strongly regular graph is a regular graph where every adjacent pair of vertices has the same number ''l'' of neighbors in common, and every non-adjacent pair of vertices has the same number ''n'' of neighbors in common. The smallest graphs that are regular but not strongly regular are the cycle graph and the circulant graph on 6 vertices. The complete graph is strongly regular for any . A theorem by Nash-Williams says that every k‑regular graph on 2k + 1 vertices has a Hamiltonian cycle. Image:0-regular_graph.svg|0-regular graph Image:1-regular_graph.svg|1-regular graph Image:2-regular_graph.svg|2-regular graph Image:3-regular_graph.svg|3-regular graph == Existence == It is well known that the necessary and sufficient conditions for a regular graph of order to exist are that and that is even. In such case it is easy to construct regular graphs by considering appropriate parameters for circulant graphs. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「regular graph」の詳細全文を読む スポンサード リンク
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