WebThe Kneser graphs are a class of graph introduced by Lovász (1978) to prove Kneser's conjecture.Given two positive integers and , the Kneser graph , often denoted (Godsil and Royle 2001; Pirnazar and Ullman 2002; Scheinerman and Ullman 2011, pp. 31-32), is the graph whose vertices represent the -subsets of , and where two vertices are connected …

{EBOOK} Geratefitness Das Lehrbuch Zur Trainerausbildung

In graph theory, the hypercube graph Qn is the graph formed from the vertices and edges of an n-dimensional hypercube. For instance, the cube graph Q3 is the graph formed by the 8 vertices and 12 edges of a three-dimensional cube. Qn has 2 vertices, 2 n edges, and is a regular graph with n edges touching each vertex. The hypercube graph Qn may also be constructed by creating a vertex for each subset of an n-el… WebA graph @C is symmetric if its automorphism group acts transitively on the arcs of @C, and s-regular if its automorphism group acts regularly on the set of s-arcs of @C. Tutte [W.T. … grinch coding.com

graph theory - How to prove connectivity $\leq$ minimum …

WebThe girth of a graph Gcontaining cycles is the length of a shortest cycle in G. The complete graph K. n. is the graph on n( 2) vertices, where every pair of vertices are adjacent. Any notation and terminology which are not explicitly de ned in this paper can be found in [5, 10]. In graph Ramsey theory, the following de nitions and notation are ... WebSep 5, 2013 · In the case of prohibited cycles explicit constructions can be used in various problems of Information Security. We observe algebraic constructions of regular graphs of large girth and graphs with large cycle indicator and describe some algorithms of Coding Theory and Cryptography based on such special families of graphs. Keywords: graphs of ... In graph theory, the girth of an undirected graph is the length of a shortest cycle contained in the graph. If the graph does not contain any cycles (that is, it is a forest), its girth is defined to be infinity. For example, a 4-cycle (square) has girth 4. A grid has girth 4 as well, and a triangular mesh has girth 3. A graph … See more A cubic graph (all vertices have degree three) of girth g that is as small as possible is known as a g-cage (or as a (3,g)-cage). The Petersen graph is the unique 5-cage (it is the smallest cubic graph of girth 5), the Heawood graph is … See more The girth of an undirected graph can be computed by running a breadth-first search from each node, with complexity $${\displaystyle O(nm)}$$ where $${\displaystyle n}$$ is the number of vertices of the graph and $${\displaystyle m}$$ is … See more For any positive integers g and χ, there exists a graph with girth at least g and chromatic number at least χ; for instance, the Grötzsch graph is triangle-free and has chromatic number … See more The odd girth and even girth of a graph are the lengths of a shortest odd cycle and shortest even cycle respectively. The circumference of a graph is the length of the longest … See more fig and feast