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A bicubic nonhamiltonian graph is a bicubic (i.e., bipartite cubic graph) that is nonhamiltonian (i.e., that does not possess a Hamiltonian cycle). Tutte (1971) conjectured ...

The Shi-Krotov-Solé graph is a weakly regular graph on 1024 vertices with regular parameters (nu,k,lambda,mu)=(1024,33,2,(0,2)). It is distance-regular but not ...

A uniquely Hamiltonian graph is a graph possessing a single Hamiltonian cycle. Classes of uniquely Hamiltonian graphs include the cycle graphs C_n, Hanoi graphs H_n, ladder ...

A lobster graph, lobster tree, or simply "lobster," is a tree having the property that the removal of leaf nodes leaves a caterpillar graph (Gallian 2007). The numbers of ...

A planar connected graph is a graph which is both planar and connected. The numbers of planar connected graphs with n=1, 2, ... nodes are 1, 1, 2, 6, 20, 99, 646, 5974, ...

Vizing's theorem states that a graph can be edge-colored in either Delta or Delta+1 colors, where Delta is the maximum vertex degree of the graph. A graph with edge chromatic ...

A two-regular graph is a regular graph for which all local degrees are 2. A two-regular graph consists of one or more (disconnected) cycles. The numbers a_n of two-regular ...

Percolation theory deals with fluid flow (or any other similar process) in random media. If the medium is a set of regular lattice points, then there are two main types of ...

The mathematical study of abstract computing machines (especially Turing machines) and the analysis of algorithms used by such machines. A connection between automata theory ...

A simple directed graph is a directed graph having no multiple edges or graph loops (corresponding to a binary adjacency matrix with 0s on the diagonal). The number of simple ...