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A quartic vertex-transitive graph is a quartic graph that is vertex transitive. Read and Wilson (1988, pp. 164-166) enumerate all connected quartic vertex-transitive graphs ...

A (0,2)-graph is a connected graph such that any two vertices have 0 or 2 common neighbors. (0,2)-graphs are regular, and the numbers of (0,2)-graphs with vertex degree 0, 1, ...

A generalized quadrangle is a generalized polygon of order 4. An order-(s,t) generalized quadrangle contains s+1 points in each line and has t+1 lines through every point, ...

A two-dimensional grid graph, also known as a rectangular grid graph or two-dimensional lattice graph (e.g., Acharya and Gill 1981), is an m×n lattice graph that is the graph ...

A white bishop graph is a graph formed from possible moves of a bishop chess piece, which may make diagonal moves of any length on a chessboard (or any other board), when ...

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 ...

The complement of a graph G, sometimes called the edge-complement (Gross and Yellen 2006, p. 86), is the graph G^', sometimes denoted G^_ or G^c (e.g., Clark and Entringer ...

The connected domination number of a connected graph G, denoted d(G), is the size of a minimum connected dominating set of a graph G. The maximum leaf number l(G) and ...

The distance polynomial is the characteristic polynomial of the graph distance matrix. The following table summarizes distance polynomials for some common classes of graphs. ...

The triangle graph is the cycle graph C_3, which is isomorphic to the complete graph K_3 as well as to the complete tripartite graph K_(3×1)=K_(1,1,1) and the triangular ...