Search Results for ""

The second Zagreb index for a graph with vertex count n and vertex degrees d_i for i=1, ..., n is defined by Z_2=sum_((i,j) in E(G))d_id_j, where E(G) is the edge set of G.

The Doob graph D(m,n) is the graph given by the graph Cartesian product of m>=1 copies of the Shrikhande graph with a Hamming graph H(n,4). Doob graphs are distance-regular ...

A graph with a finite number of nodes and edges. If it has n nodes and has no multiple edges or graph loops (i.e., it is simple), it is a subgraph of the complete graph K_n. ...

A graph G is hypohamiltonian if G is nonhamiltonian, but G-v is Hamiltonian for every v in V (Bondy and Murty 1976, p. 61). The Petersen graph, which has ten nodes, is the ...

The fork graph, sometimes also called the chair graph, is the 5-vertex tree illustrated above. It could perhaps also be known as the 'h graph' (but not to be confused with ...

A unit-distance graph is a distance graph having an embedding in the Euclidean plane (unit-distance embedding) in which vertices are distinct points and all edges are of ...

The paw graph is the 3-pan graph, which is also isomorphic to the (3,1)-tadpole graph. It is implemented in the Wolfram Language as GraphData["PawGraph"].

The banner graph is the (4,1)-tadpole graph illustrated above. It could perhaps also be termed the 'P graph.' It is implemented in the Wolfram Language as ...

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 ...

A mixed graph in which both directed and undirected edges may exist. If only directed edges exist, the graph is called a directed graph. If only undirected edges exist, it is ...