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The Folkman graph, a quartic graph with 20 vertices, the smallest semi-symmetric graph. [3] The Meredith graph, a quartic graph with 70 vertices that is 4-connected but has no Hamiltonian cycle, disproving a conjecture of Crispin Nash-Williams. [4] Every medial graph is a quartic plane graph, and every quartic plane graph is the medial graph of ...
This sortable list points to the articles describing various individual (finite) graphs. [1] The columns 'vertices', 'edges', ' radius ', ' diameter ', ' girth ', 'P' (whether the graph is planar ), χ ( chromatic number ) and χ' ( chromatic index ) are also sortable, allowing to search for a parameter or another.
Switching {X,Y} in a graph. A two-graph is equivalent to a switching class of graphs and also to a (signed) switching class of signed complete graphs.. Switching a set of vertices in a (simple) graph means reversing the adjacencies of each pair of vertices, one in the set and the other not in the set: thus the edge set is changed so that an adjacent pair becomes nonadjacent and a nonadjacent ...
Regular graphs of degree at most 2 are easy to classify: a 0-regular graph consists of disconnected vertices, a 1-regular graph consists of disconnected edges, and a 2-regular graph consists of a disjoint union of cycles and infinite chains. A 3-regular graph is known as a cubic graph.
A multigraph with multiple edges (red) and several loops (blue). Not all authors allow multigraphs to have loops. In mathematics, and more specifically in graph theory, a multigraph is a graph which is permitted to have multiple edges (also called parallel edges [1]), that is, edges that have the same end nodes.
The complement graph of a complete graph is an empty graph. If the edges of a complete graph are each given an orientation, the resulting directed graph is called a tournament. K n can be decomposed into n trees T i such that T i has i vertices. [6] Ringel's conjecture asks if the complete graph K 2n+1 can be decomposed into copies of any tree ...
It is possible to approximate the diameter of a weighted graph to within an approximation ratio of 3/2, in time ~ ((/, /), where the ~ notation hides logarithmic factors in the time bound. [6] Under the exponential time hypothesis, no substantially more accurate approximation, substantially faster than all pairs shortest paths, is possible.
A cycle basis of the graph is a set of simple cycles that forms a basis of the cycle space. [2] Using ideas from algebraic topology, the binary cycle space generalizes to vector spaces or modules over other rings such as the integers, rational or real numbers, etc. [3]