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The arc set of a directed graph is the set of all arcs (directed edges) of the graph. The arc set for a directed graph g is given in the Wolfram Language by EdgeList[g].

The König-Egeváry theorem, sometimes simply called König's theorem, asserts that the matching number (i.e., size of a maximum independent edge set) is equal to the vertex ...

The energy of a graph is defined as the sum of the absolute values of its graph eigenvalues (i.e., the sum of its graph spectrum terms). Other varieties of graph energy are ...

A connected graph having e graph edges is said to be sequential if it is possible to label the nodes i with distinct integers f_i in {0,1,2,...,e-1} such that when graph edge ...

The Suetake graph is a weakly regular Hamiltonian graph on 231 vertices with parameters (nu,k,lambda,mu)=(72,(12),(0),(0,4)). It is distance-regular with intersection array ...

The Norton-Smith graph is a weakly regular graph on 1134 vertices with regular parameters (nu,k,lambda,mu)=(1134,117,36,(0,12)). It is distance-regular as well as ...

An (n,k)-firecracker is a graph obtained by the concatenation of n k-stars by linking one leaf from each (Chen et al. 1997, Gallian 2007). Firecracker graphs are graceful ...

The radius of a graph is the minimum graph eccentricity of any graph vertex in a graph. A disconnected graph therefore has infinite radius (West 2000, p. 71). Graph radius is ...

An alkane graph is a tree in which vertices correspond to atoms and edges to carbon-carbon or hydrogen-carbon bonds in a chemical alkane. In chemistry, an alkane is an ...

A stacked (or generalized) prism graph Y_(m,n) is a simple graph given by the graph Cartesian product Y_(m,n)=C_m square P_n (Gallian 2007) for positive integers m,n with ...