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A matchstick graph is a simple graph which has a graph embedding that is planar, for which all distances between vertices have unit distance, and which is non-degenerate (so ...

The word "graph" has (at least) two meanings in mathematics. In elementary mathematics, "graph" refers to a function graph or "graph of a function," i.e., a plot. In a ...

Every point which can be constructed with a straightedge and compass, and no other points, can be constructed using identical matchsticks (i.e., identical movable line ...

The gear graph, also sometimes known as a bipartite wheel graph (Brandstädt et al. 1987), is a wheel graph with a graph vertex added between each pair of adjacent graph ...

The Harborth graph is the smallest known 4-regular matchstick graph. It is therefore both planar and unit-distance. It has 104 edges and 52 vertices. This graph was named ...

The triangular snake graph TS_n is the graph on n vertices with n odd defined by starting with the path graph P_(n-1) and adding edges (2i-1,2i+1) for i=1, ..., n-1. The ...

The n-sunlet graph is the graph on 2n vertices obtained by attaching n pendant edges to a cycle graph C_n (ISGCI), i.e., the coronas C_n circledot K_1 (Frucht 1979). Sunlet ...

A kayak paddle graph KP(k,m,l) is the graph obtained by joining cycle graphs C_k and C_m by a path of length l (Gallian 2018). KP(3,3,1) is isomorphic to the 3-barbell graph. ...

A unit-distance embedding is a graph embedding in which all edges have unit length. A graph possessing a unit-distance embedding in two dimensions is called a unit-distance ...

The Jahangir graph J_(n,m) is a kind of generalized wheel graph with consisting of mn circular vertices and a central vertex connected to every mth vertex around the circle. ...