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The degree or valency of a vertex is the number of edges that are incident to it, where a loop is counted twice. The degree of a graph is the maximum of the degrees of its vertices. In an undirected simple graph of order n, the maximum degree of each vertex is n − 1 and the maximum size of the graph is n(n − 1) / 2 .
Hexagonal paper shows regular hexagons instead of squares. These can be used to map geometric tiled or tesselated designs among other uses. Isometric graph paper or 3D graph paper is a triangular graph paper which uses a series of three guidelines forming a 60° grid of small triangles. The triangles are arranged in groups of six to make hexagons.
Isometric graph paper can be placed under a normal piece of drawing paper to help achieve the effect without calculation. In a similar way, an isometric view can be obtained in a 3D scene. Starting with the camera aligned parallel to the floor and aligned to the coordinate axes, it is first rotated horizontally (around the vertical axis) by ± ...
Below is the table of the vertex numbers for the best-known graphs (as of June 2024) in the undirected degree diameter problem for graphs of degree at most 3 ≤ d ≤ 16 and diameter 2 ≤ k ≤ 10. Only a few of the graphs in this table (marked in bold) are known to be optimal (that is, largest possible).
The maximum degree of a graph is denoted by (), and is the maximum of 's vertices' degrees. The minimum degree of a graph is denoted by (), and is the minimum of 's vertices' degrees. In the multigraph shown on the right, the maximum degree is 5 and the minimum degree is 0. In a regular graph, every vertex has the same degree, and so we can ...
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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]
The Petersen graph (diameter 2, girth 5, degree 3, order 10) The Hoffman–Singleton graph (diameter 2, girth 5, degree 7, order 50) A hypothetical graph (or more than one) of diameter 2, girth 5, degree 57 and order 3250; the existence of such is unknown and is one of the most famous open problems in graph theory. [4]