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:
“I consider, then, the power to annul a law of the United States, assumed by one state, incompatible with the existence of the Union, contradicted expressly by the letter of the Constitution, unauthorized by its spirit, inconsistent with every principle on which it was founded, and destructive of the great object for which it was formed.”
—Andrew Jackson (1767–1845)
“As for types like my own, obscurely motivated by the conviction that our existence was worthless if we didn’t make a turning point of it, we were assigned to the humanities, to poetry, philosophy, painting—the nursery games of humankind, which had to be left behind when the age of science began. The humanities would be called upon to choose a wallpaper for the crypt, as the end drew near.”
—Saul Bellow (b. 1915)
“For it is only as an aesthetic phenomenon that existence and the world are eternally justified.”
—Friedrich Nietzsche (1844–1900)