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Johnson Graph
In mathematics, Johnson graphs are a special class of undirected graphs defined from systems of sets. The vertices of the Johnson graph J(n,k) are the k-element subsets of an n-element set; two vertices are adjacent when the intersection of the two vertices (subsets) contains (k-1)-elements.. Both Johnson graphs and the closely related Johnson scheme are named after Selmer M. Johnson. Special cases *Both J(n,1) and J(n,n-1) are the complete graph . *J(4,2) is the octahedral graph. *J(5,2) is the complement of the Petersen graph, hence the line graph of . More generally, for all n, the Johnson graph J(n,2) is the line graph of and the complement of the Kneser graph K(n,2). Graph-theoretic properties * J(n,k) is isomorphic to J(n,n-k). * For all 0 \leq j \leq \operatorname(J(n,k)), any pair of vertices at distance j share k-j elements in common. * J(n,k) is Hamilton-connected, meaning that every pair of vertices forms the endpoints of a Hamiltonian path in the graph. In parti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johnson Graph J(5,2)
Johnson may refer to: People and fictional characters *Johnson (surname), a common surname in English *Johnson (given name), a list of people * List of people with surname Johnson, including fictional characters *Johnson (composer) (1953–2011), Indian film score composer *Johnson (rapper) (born 1979), Danish rapper *Mr. Johnson (born 1966), Nigerian singer Places * Mount Johnson (other) Canada * Johnson, Ontario, township * Johnson (electoral district), provincial electoral district in Quebec * Johnson Point (British Columbia), a headland on the north side of the entrance to Belize Inlet United States * Johnson, Arizona * Johnson, Arkansas, a town * Johnson, Delaware * Johnson, Indiana, an unincorporated town * Johnson, Kentucky * Johnson, Minnesota * Johnson, Nebraska * Johnson, New York * Johnson, Ohio, an unincorporated community * Johnson, Oklahoma * Johnson, Utah * Johnson, Vermont, a town ** Johnson (village), Vermont * Johnson, Washington * Johnson, Wisconsin, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |