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The utility problem posits three houses and three utility companies--say, gas, electric, and water--and asks if each utility can be connected to each house without having any ...
An empty graph on n nodes consists of n isolated nodes with no edges. Such graphs are sometimes also called edgeless graphs or null graphs (though the term "null graph" is ...
The Balaban 10-cage is one of the three (3,10)-cage graphs (Read and Wilson 1998, p. 272). The Balaban (3,10)-cage was the first known example of a 10-cage (Balaban 1973, ...
The banner graph is the (4,1)-tadpole graph illustrated above. It could perhaps also be termed the 'P graph.' It is implemented in the Wolfram Language as ...
The Harries-Wong graph is one of the three (3,10)-cage graphs, the other two being the (10,3)-cage known as the Balaban 10-cage and the Harries graph. The Harries-Wong graph ...
The Harries graph is one of the three (3,10)-cage graphs, the other two being the (10,3)-cage known as the Balaban 10-cage and the Harries-Wong graph. The Harries graph is ...
The Perkel graph is a weakly regular graph on 57 vertices and 171 edges, shown above in several embeddings. It is the unique distance-regular graph with intersection array ...
The tetragonal antiwedge graph is the skeleton of the tetragonal antiwedge. It is a has 6 vertices, 10 edges, and 6 faces. The tetragonal antiwedge graph is self-dual and is ...
The Folkman graph is a semisymmetric graph that has the minimum possible number of nodes (20) (Skiena 1990, p. 186). It is implemented in the Wolfram Language as ...
The Celmins-Swart snarks are the two snarks on 26 vertices and 39 edges illustrated above. They are implemented in the Wolfram Language as GraphData["CelminsSwartSnark1"] and ...
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