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.
Read more about this topic: Regular Graph
Famous quotes containing the word existence:
“The light that radiates from the great novels time can never dim, for human existence is perpetually being forgotten by man and thus the novelists’ discoveries, however old they may be, will never cease to astonish.”
—Milan Kundera (b. 1929)
“For believe me!—the secret to harvesting the greatest abundance and the greatest enjoyment from existence is this—living dangerously! Build your cities on the slopes of Vesuvius! Send your ships into uncharted seas! Live at war with your peers and yourselves! Be robbers and conquerors, so long as you cannot be rulers and possessors, you knowing ones! The time will soon be past when you could be content to live hidden in the forests like timid deer.”
—Friedrich Nietzsche (1844–1900)
“Justice begins with the recognition of the necessity of sharing. The oldest law is that which regulates it, and this is still the most important law today and, as such, has remained the basic concern of all movements which have at heart the community of human activities and of human existence in general.”
—Elias Canetti (b. 1905)