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An edge subdivision is the insertion of a new vertex v_j in the middle of an exiting edge e=v_iv_k accompanied by the joining of the original edge endpoints with the new ...

A graph G that becomes disconnected when removing a suitable complete subgraph K, called a vertex cut, is said to be quasiseparable. The two simplest cases are those where K ...

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 ...

An edge-magic graph is a labeled graph with e graph edges labeled with distinct elements {1,2,...,e} so that the sum of the graph edge labels at each graph vertex is the ...

The tetrakis hexahedral graph is Archimedean dual graph which is the skeleton of the disdyakis triacontahedron. It is implemented in the Wolfram Language as ...

A lattice graph, also known as a mesh graph or grid graph, is a graph possessing an embedding in a Euclidean space R^n that forms a regular tiling. Examples include grid ...

The Errera graph is the 17-node planar graph illustrated above that tangles the Kempe chains in Kempe's algorithm and thus provides an example of how Kempe's supposed proof ...

A regular graph that is not strongly regular is known as a weakly regular graph. There are no weakly regular simple graphs on fewer than six nodes, and the numbers on n=6, 7, ...

A transposition graph G_n is a graph whose nodes correspond to permutations and edges to permutations that differ by exactly one transposition (Skiena 1990, p. 9, Clark ...

Given a planar graph G, its geometric dual G^* is constructed by placing a vertex in each region of G (including the exterior region) and, if two regions have an edge x in ...