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A graph G whose line graph is L(G) is called the root graph R(L(G)) of L(G). In order words, R(L(G))=G. The root graph of a connected graph is unique except for K_3=C_3 (the ...

A graph G having chromatic number gamma(G)=k is called a k-chromatic graph (Harary 1994, p. 127). In contrast, a graph having gamma(G)<=k is said to be a k-colorable graph. A ...

The center of a graph G is the set of vertices of graph eccentricity equal to the graph radius (i.e., the set of central points). In the above illustration, center nodes are ...

A 1-factor of a graph G with n graph vertices is a set of n/2 separate graph edges which collectively contain all n of the graph vertices of G among their endpoints.

A connected labeled graph with n graph edges in which all graph vertices can be labeled with distinct integers (mod n) so that the sums of the pairs of numbers at the ends of ...

The cyclotomic graph of order q with q a prime power is a graph on q nodes with two nodes adjacent if their difference is a cube in the finite field GF(q). This graph is ...

The Dyck graph is unique cubic symmetric graph on 32 nodes, illustrated above in a number of embeddings. It is denoted F_(032)A in the Foster census of cubic symmetric graphs ...

The m×n queen graph Q_(m,n) is a graph with mn vertices in which each vertex represents a square in an m×n chessboard, and each edge corresponds to a legal move by a queen. ...

A graph with graph edges of two possible "colors," usually identified as red and blue. For a bichromatic graph with R red graph edges and B blue graph edges, R+B>=2.

The deltoidal hexecontahedral graph is an Archimedean dual graph which is the skeleton of the deltoidal hexecontahedron as well as the rhombic hexecontahedron. It is ...