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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).
In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points ) which are connected by edges (also called arcs , links or lines ).
A claw. In graph theory, an area of mathematics, a claw-free graph is a graph that does not have a claw as an induced subgraph.. A claw is another name for the complete bipartite graph, (that is, a star graph comprising three edges, three leaves, and a central vertex).
This notion has made it possible to use the methods of graph theory in universal algebra and several other areas of discrete mathematics and computer science.Graph algebras have been used, for example, in constructions concerning dualities, [2] equational theories, [3] flatness, [4] groupoid rings, [5] topologies, [6] varieties, [7] finite-state machines, [8] [9] tree languages and tree ...
In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency. A regular directed graph must also satisfy the stronger condition that the indegree and outdegree of each internal vertex are equal to each other. [1]
The cube of every connected graph necessarily contains a Hamiltonian cycle. [10] It is not necessarily the case that the square of a connected graph is Hamiltonian, and it is NP-complete to determine whether the square is Hamiltonian. [11] Nevertheless, by Fleischner's theorem, the square of a 2-vertex-connected graph is always Hamiltonian. [12]