High Quality Content by WIKIPEDIA articles! In the mathematical field of graph theory, the odd graph On is the graph whose vertex set contains all n ? 1-element subsets of X = {1,2,...2n ? 1} and in which an edge connects two vertices iff the corresponding subsets are disjoint. It has tbinom {2n-1}{n-1} vertices and ntbinom {2n-1}{n-1}/2 edges. Therefore, the number of vertices for n = 1, 2,... is 1, 3, 10, 35, 126, 462, 1716, 6435 (sequence A001700 in OEIS). An odd graph is regular of degree n, and it is also distance transitive, hence distance regular. The most familiar example of an odd graph is the Petersen graph, which is O3, while O2 is the triangle.

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