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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 ± ...
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.
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 .
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.
Two non-isomorphic graphs with the same degree sequence (3, 2, 2, 2, 2, 1, 1, 1). The degree sequence of an undirected graph is the non-increasing sequence of its vertex degrees; [5] for the above graph it is (5, 3, 3, 2, 2, 1, 0). The degree sequence is a graph invariant, so isomorphic graphs have the same degree sequence. However, the degree ...
The degree sequence of a directed graph is the list of its indegree and outdegree pairs; for the above example we have degree sequence ((2, 0), (2, 2), (0, 2), (1, 1)). The degree sequence is a directed graph invariant so isomorphic directed graphs have the same degree sequence.
In this graph, an even number of vertices (the four vertices numbered 2, 4, 5, and 6) have odd degrees. The sum of degrees of all six vertices is 2 + 3 + 2 + 3 + 3 + 1 = 14, twice the number of edges.
An example graph, with the properties of being planar and being connected, and with order 6, size 7, diameter 3, girth 3, vertex connectivity 1, and degree sequence <3, 3, 3, 2, 2, 1> In graph theory , a graph property or graph invariant is a property of graphs that depends only on the abstract structure, not on graph representations such as ...
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