Search results
Results from the WOW.Com Content Network
In graph theory, reachability refers to the ability to get from one vertex to another within a graph. A vertex s {\displaystyle s} can reach a vertex t {\displaystyle t} (and t {\displaystyle t} is reachable from s {\displaystyle s} ) if there exists a sequence of adjacent vertices (i.e. a walk ) which starts with s {\displaystyle s} and ends ...
In graph theory, a deletion-contraction formula / recursion is any formula of the following recursive form: = + (/). Here G is a graph, f is a function on graphs, e is any edge of G, G \ e denotes edge deletion, and G / e denotes contraction. Tutte refers to such a function as a W-function. [1]
The computation of (1 + iπ / N ) N is displayed as the combined effect of N repeated multiplications in the complex plane, with the final point being the actual value of (1 + iπ / N ) N. It can be seen that as N gets larger (1 + iπ / N ) N approaches a limit of −1. Euler's identity asserts that is
Exponential functions y = 2 x and y = 4 x intersect the graph of y = x + 1, respectively, at x = 1 and x = -1/2. The number e is the unique base such that y = e x intersects only at x = 0. We may infer that e lies between 2 and 4. The number e is the unique real number such that (+) < < (+) + for all positive x. [31]
In an undirected simple graph of order n, the maximum degree of each vertex is n − 1 and the maximum size of the graph is n(n − 1) / 2 . The edges of an undirected simple graph permitting loops G {\displaystyle G} induce a symmetric homogeneous relation ∼ {\displaystyle \sim } on the vertices of G {\displaystyle G} that is called ...
A hypergraph H may be represented by a bipartite graph BG as follows: the sets X and E are the parts of BG, and (x 1, e 1) are connected with an edge if and only if vertex x 1 is contained in edge e 1 in H. Conversely, any bipartite graph with fixed parts and no unconnected nodes in the second part represents some hypergraph in the manner ...
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
This is why this algorithm is useful. [4] If a graph contains a "negative cycle" (i.e. a cycle whose edges sum to a negative value) that is reachable from the source, then there is no cheapest path: any path that has a point on the negative cycle can be made cheaper by one more walk around the negative cycle. In such a case, the Bellman–Ford ...