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The Georges graph, illustrated above, is 50-node graph which is the smallest currently known example of a 3-connected bicubic nonhamiltonian graph. It is implemented in the ...

A column-convex self-avoiding polygon which contains the bottom edge of its minimal bounding rectangle. The anisotropic perimeter and area generating function ...

A prism graph, denoted Y_n, D_n (Gallian 1987), or Pi_n (Hladnik et al. 2002), and sometimes also called a circular ladder graph and denoted CL_n (Gross and Yellen 1999, p. ...

A shortest path between two graph vertices (u,v) of a graph (Skiena 1990, p. 225). There may be more than one different shortest paths, all of the same length. Graph ...

A chordless graph is a simple graph possessing no chords. A chordal graph (which possesses no chordless cycles) is not the same as (or converse of) a chordless graph (which ...

An integral graph, not to be confused with an integral embedding of a graph, is defined as a graph whose graph spectrum consists entirely of integers. The notion was first ...

A graph G is called d-polytopal if there exists a d-dimensional convex polytope P such that the vertices and edges of G are in a one-to-one incidence-preserving ...

As defined in this work, a wheel graph W_n of order n, sometimes simply called an n-wheel (Harary 1994, p. 46; Pemmaraju and Skiena 2003, p. 248; Tutte 2005, p. 78), is a ...

The graph product denoted G-H and defined by the adjacency relations (gadjg^') or (g=g^' and hadjh^'). The graph lexicographic product is also known as the graph composition ...

A bicubic graph is a bipartite cubic graph. Tutte (1971) conjectured that all 3-connected bicubic graphs are Hamiltonian (the Tutte conjecture), but a number of bicubic ...