Search results
Results from the WOW.Com Content Network
While each non-complete word-representable graph G is 2(n − κ(G))-representable, where κ(G) is the size of a maximal clique in G, [7] the highest known representation number is floor(n/2) given by crown graphs with an all-adjacent vertex. [7] Interestingly, such graphs are not the only graphs that require long representations. [15]
Therefore, each vector 1 E(v) is a 1-by-m vector in which element e is 1 if edge e is adjacent to v, and 0 otherwise. The incidence matrix of the graph, denoted by A G, is an n-by-m matrix in which each row v is the incidence vector 1 E(V). In other words, each element v,e in the matrix is 1 if node v is adjacent to edge e, and 0 otherwise.
The open neighborhood of v in G may be denoted N G (v) or N(v), and the closed neighborhood may be denoted N G [v] or N[v]. When the openness or closedness of a neighborhood is not specified, it is assumed to be open. network A graph in which attributes (e.g. names) are associated with the nodes and/or edges. node A synonym for vertex. non-edge
The California Job Case was a compartmentalized box for printing in the 19th century, sizes corresponding to the commonality of letters. The frequency of letters in text has been studied for use in cryptanalysis, and frequency analysis in particular, dating back to the Arab mathematician al-Kindi (c. AD 801–873 ), who formally developed the method (the ciphers breakable by this technique go ...
A graph that contains a Hamiltonian path is called a traceable graph. A graph is Hamiltonian-connected if for every pair of vertices there is a Hamiltonian path between the two vertices. A Hamiltonian cycle, Hamiltonian circuit, vertex tour or graph cycle is a cycle that visits each vertex exactly once.
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
The complete graph on n vertices is denoted by K n.Some sources claim that the letter K in this notation stands for the German word komplett, [4] but the German name for a complete graph, vollständiger Graph, does not contain the letter K, and other sources state that the notation honors the contributions of Kazimierz Kuratowski to graph theory.
If the graph is furthermore planar the same paper gives an O(n) algorithm. Their O(n log 4 n) time bound can be improved based on subsequent improvements to the time for maintaining the set of bridges in a dynamic graph. [7] Further improvements, reducing the time bound to O(n log 2 n) or (with additional randomized data structures) O(n log n ...