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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]
In mathematics and computer science, graph theory is the study of graphs, ... a decomposition of a regular graph into regular subgraphs of given degrees; Graph classes
3. A strongly regular graph is a regular graph in which every two adjacent vertices have the same number of shared neighbours and every two non-adjacent vertices have the same number of shared neighbours. 4. A strongly chordal graph is a chordal graph in which every even cycle of length six or more has an odd chord. 5.
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 graph theory, the girth of an undirected graph is the length of a shortest cycle contained in the graph. [1] If the graph does not contain any cycles (that is, it is a forest), its girth is defined to be infinity. [2] For example, a 4-cycle (square) has girth 4. A grid has girth 4 as well, and a triangular mesh has girth 3.
The hemi-dodecahedron is a regular map produced by pentagonal embedding of the Petersen graph in the projective plane. The p-hosohedron is a regular map of type {2,p}. The Dyck map is a regular map of 12 octagons on a genus-3 surface. Its underlying graph, the Dyck graph, can also form a regular map of 16 hexagons in a torus.
The Petersen graph is a cubic graph. The complete bipartite graph, is an example of a bicubic graph. In the mathematical field of graph theory, a cubic graph is a graph in which all vertices have degree three. In other words, a cubic graph is a 3-regular graph. Cubic graphs are also called trivalent graphs.
In the mathematical field of graph theory, a distance-regular graph is a regular graph such that for any two vertices v and w, the number of vertices at distance j from v and at distance k from w depends only upon j, k, and the distance between v and w. Some authors exclude the complete graphs and disconnected graphs from this definition.
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