Relation To Minimum Vertex Degree
Minimum vertex degree gives a trivial upper bound on edge-connectivity. That is, if a graph G = (E,V) is k-edge-connected then it is necessary that k ≤ δ(G), where δ(G) is the minimum degree of any vertex v ∈ V. Obviously, deleting all edges incident to a vertex, v, would then disconnect v from the graph.
Read more about this topic: K-edge-connected Graph
Famous quotes containing the words relation to, relation, minimum and/or degree:
“... a worker was seldom so much annoyed by what he got as by what he got in relation to his fellow workers.”
—Mary Barnett Gilson (1877–?)
“Every word was once a poem. Every new relation is a new word.”
—Ralph Waldo Emerson (1803–1882)
“After decades of unappreciated drudgery, American women just don’t do housework any more—that is, beyond the minimum that is required in order to clear a path from the bedroom to the front door so they can get off to work in the mourning.”
—Barbara Ehrenreich (20th century)
“The real essence, the internal qualities, and constitution of even the meanest object, is hid from our view; something there is in every drop of water, every grain of sand, which it is beyond the power of human understanding to fathom or comprehend. But it is evident ... that we are influenced by false principles to that degree as to mistrust our senses, and think we know nothing of those things which we perfectly comprehend.”
—George Berkeley (1685–1753)