Search Results for ""

The complement of a graph G, sometimes called the edge-complement (Gross and Yellen 2006, p. 86), is the graph G^', sometimes denoted G^_ or G^c (e.g., Clark and Entringer ...

The graph complement of a graph hole. Graph antiholes are called even if they have an even number of vertices and odd if they have an odd number of vertices (Chvátal). No odd ...

A two-regular graph is a regular graph for which all local degrees are 2. A two-regular graph consists of one or more (disconnected) cycles. The numbers a_n of two-regular ...

The circumference of a graph is the length of any longest cycle in a graph. Hamiltonian graphs on n>1 vertices therefore have circumference of n. For a cyclic graph, the ...

The graph difference of graphs G and H is the graph with adjacency matrix given by the difference of adjacency matrices of G and H. A graph difference is defined when the ...

A cubic symmetric graph is a symmetric cubic (i.e., regular of order 3). Such graphs were first studied by Foster (1932). They have since been the subject of much interest ...

A double-toroidal graph is a graph with graph genus 2 (West 2000, p. 266). Planar and toroidal graphs are therefore not double-toroidal. Some known double-toroidal graphs on ...

The graph neighborhood of a vertex v in a graph is the set of all the vertices adjacent to v including v itself. More generally, the ith neighborhood of v is the set of all ...

A section of a graph obtained by finding its intersection with a plane.

The double graph of a given graph G is constructed by making two copies of G (including the initial edge set of each) and adding edges u_1v_2 and v_1u_2 for every edge uv of ...