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A cactus graph, sometimes also called a cactus tree, a mixed Husimi tree, or a polygonal cactus with bridges, is a connected graph in which any two graph cycles have no edge ...

The Gewirtz graph, sometimes also called the Sims-Gewirtz graph (Brouwer), is an integral graph on 56 nodes and 280 edges that is also a regular graph of order 10. It is ...

A cycle of a graph G, also called a circuit if the first vertex is not specified, is a subset of the edge set of G that forms a path such that the first node of the path ...

The Suzuki graph is an edge-transitive strongly regular graph on 1782 vertices with parameters (nu,k,lambda,mu)=(1782,416,100,96) and automorphism group Suz.2. It is an ...

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 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 ...

A one-dimensional line segment where two two-dimensional faces of an n-dimensional polytope meet, also called a side.

The composition G=G_1[G_2] of graphs G_1 and G_2 with disjoint point sets V_1 and V_2 and edge sets X_1 and X_2 is the graph with point vertex V_1×V_2 and u=(u_1,u_2) ...

An automorphism of a graph is a graph isomorphism with itself, i.e., a mapping from the vertices of the given graph G back to vertices of G such that the resulting graph is ...

A bipartite graph, also called a bigraph, is a set of graph vertices decomposed into two disjoint sets such that no two graph vertices within the same set are adjacent. A ...