Signed Graph - Examples

Examples

  • The complete signed graph on n vertices with loops, denoted by ±Kno, has every possible positive and negative edge including negative loops, but no positive loops. Its edges correspond to the roots of the root system Cn; the column of an edge in the incidence matrix (see below) is the vector representing the root.
  • The complete signed graph with half-edges, ±Kn', is ±Kn with a half-edge at every vertex. Its edges correspond to the roots of the root system Bn, half-edges corresponding to the unit basis vectors.
  • The complete signed link graph, ±Kn, is the same but without loops. Its edges correspond to the roots of the root system Dn.
  • An all-positive signed graph has only positive edges. If the underlying graph is G, the all-positive signing is written +G.
  • An all-negative signed graph has only negative edges. It is balanced if and only if it is bipartite because a circle is positive if and only if it has even length. An all-negative graph with underlying graph G is written −G.
  • A signed complete graph has as underlying graph G the ordinary complete graph Kn. It may have any signs. Signed complete graphs are equivalent to two-graphs, which are of value in finite group theory. A two-graph can be defined as the class of vertex sets of negative triangles in a signed complete graph.

Read more about this topic:  Signed Graph

Famous quotes containing the word examples:

    “Histories are more full of examples of the fidelity of dogs than of friends.”
    —Alexander Pope (1688–1744)

    “No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
    —André Breton (1896–1966)

    “It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
    —G.C. (Georg Christoph)