graph.famous          package:igraph          R Documentation(utf8)

_C_r_e_a_t_i_n_g _n_a_m_e_d _g_r_a_p_h_s

_D_e_s_c_r_i_p_t_i_o_n:

     There are some famous, named graphs, sometimes counterexamples to
     some conjecture or unique graphs with given features. These can be
     created with this function

_U_s_a_g_e:

     graph.famous(name)

_A_r_g_u_m_e_n_t_s:

    name: Character constant giving the name of the graph. It is case
          insensitive.

_D_e_t_a_i_l_s:

     'graph.famous' knows the following graphs:

   _B_u_l_l The bull graph, 5 vertices, 5 edges, resembles to the head of a
        bull if drawn properly.

   _C_h_v_a_t_a_l This is the smallest triangle-free graph that is both
        4-chromatic and 4-regular. According to the Grunbaum conjecture
        there exists an m-regular, m-chromatic graph with n vertices
        for every m>1 and n>2. The Chvatal graph is an example for m=4
        and n=12. It has 24 edges.

   _C_o_x_e_t_e_r A non-Hamiltonian cubic symmetric graph with 28 vertices and
        42 edges.

   _C_u_b_i_c_a_l The Platonic graph of the cube. A convex regular polyhedron
        with 8 vertices and 12 edges.

   _D_i_a_m_o_n_d A graph with 4 vertices and 5 edges, resembles to a
        schematic diamond if drawn properly.

   _D_o_d_e_c_a_h_e_d_r_a_l, _D_o_d_e_c_a_h_e_d_r_o_n Another Platonic solid with 20 vertices
        and 30 edges.

   _F_o_l_k_m_a_n The semisymmetric graph with minimum number of vertices, 20
        and 40 edges. A semisymmetric graph is regular, edge transitive
        and not vertex transitive.

   _F_r_a_n_k_l_i_n This is a graph whose embedding to the Klein bottle can be
        colored with six colors, it is a counterexample to the
        neccessity of the Heawood conjecture on a Klein bottle. It has
        12 vertices and 18 edges.

   _F_r_u_c_h_t The Frucht Graph is the smallest cubical graph whose
        automorphism group consists only of the identity element. It
        has 12 vertices and 18 edges.

   _G_r_o_t_z_s_c_h The Grötzsch graph is a triangle-free graph with 11
        vertices, 20 edges, and chromatic number 4. It is named after
        German mathematician Herbert Grötzsch, and its existence
        demonstrates that the assumption of planarity is necessary in
        Grötzsch's theorem that every triangle-free planar graph is
        3-colorable.

   _H_e_a_w_o_o_d The Heawood graph is an undirected graph with 14 vertices
        and 21 edges. The graph is cubic, and all cycles in the graph
        have six or more edges. Every smaller cubic graph has shorter
        cycles, so this graph is the 6-cage, the smallest cubic graph
        of girth 6.

   _H_e_r_s_c_h_e_l The Herschel graph is the smallest nonhamiltonian
        polyhedral graph. It is the unique such graph on 11 nodes, and
        has 18 edges.

   _H_o_u_s_e The house graph is a 5-vertex, 6-edge graph, the schematic
        draw of a house if drawn properly, basicly a  triangle of the
        top of a square.

   _H_o_u_s_e_X The same as the house graph with an X in the square. 5
        vertices and 8 edges.

   _I_c_o_s_a_h_e_d_r_a_l, _I_c_o_s_a_h_e_d_r_o_n A Platonic solid with 12 vertices and 30
        edges.

   _K_r_a_c_k_h_a_r_d_t__K_i_t_e A social network with 10 vertices and 18 edges.
        Krackhardt, D. Assessing the Political Landscape: Structure,
        Cognition, and Power in Organizations. Admin. Sci. Quart. 35,
        342-369, 1990.

   _L_e_v_i The graph is a 4-arc transitive cubic graph, it has 30 vertices
        and 45 edges.

   _M_c_G_e_e The McGee graph is the unique 3-regular 7-cage graph, it has
        24 vertices and 36 edges.

   _M_e_r_e_d_i_t_h The Meredith graph is a quartic graph on 70 nodes and 140
        edges that is a counterexample to the conjecture that every
        4-regular 4-connected graph is Hamiltonian.

   _N_o_p_e_r_f_e_c_t_m_a_t_c_h_i_n_g A connected graph with 16 vertices and 27 edges
        containing no perfect matching. A matching in a graph is a set
        of pairwise non-adjacent edges; that is, no two edges share a
        common vertex. A perfect matching is a matching which covers
        all vertices of the graph.

   _N_o_n_l_i_n_e A graph whose connected components are the 9 graphs whose
        presence as a vertex-induced subgraph in a graph makes a
        nonline graph. It has 50 vertices and 72 edges.

   _O_c_t_a_h_e_d_r_a_l, _O_c_t_a_h_e_d_r_o_n Platonic solid with 6 vertices and 12 edges. 

   _P_e_t_e_r_s_e_n A 3-regular graph with 10 vertices and 15 edges. It is the
        smallest hypohamiltonian graph, ie. it is non-hamiltonian but
        removing any single vertex from it makes it Hamiltonian.

   _R_o_b_e_r_t_s_o_n The unique (4,5)-cage graph, ie. a 4-regular graph of
        girth 5. It has 19 vertices and 38 edges.

   _S_m_a_l_l_e_s_t_c_y_c_l_i_c_g_r_o_u_p A smallest nontrivial graph whose automorphism
        group is cyclic. It has 9 vertices and 15 edges.

   _T_e_t_r_a_h_e_d_r_a_l, _T_e_t_r_a_h_e_d_r_o_n Platonic solid with 4 vertices and 6 edges.

   _T_h_o_m_a_s_s_e_n The smallest hypotraceable graph, on 34 vertices and 52
        edges. A hypotracable graph does not contain a Hamiltonian path
        but after removing any single vertex from it the remainder
        always contains a Hamiltonian path. A graph containing a
        Hamiltonian path is called tracable.

   _T_u_t_t_e Tait's Hamiltonian graph conjecture states that every
        3-connected 3-regular planar graph is Hamiltonian. This graph
        is a counterexample. It has 46 vertices and 69 edges.

   _U_n_i_q_u_e_l_y_3_c_o_l_o_r_a_b_l_e Returns a 12-vertex, triangle-free graph with
        chromatic number 3 that is uniquely 3-colorable.

   _W_a_l_t_h_e_r An identity graph with 25 vertices and 31 edges. An identity
        graph has a single graph automorphism, the trivial one.

_V_a_l_u_e:

     A graph object.

_A_u_t_h_o_r(_s):

     Gabor Csardi csardi@rmki.kfki.hu

_S_e_e _A_l_s_o:

     'graph' can create arbitrary graphs, see also the other functions
     on the its manual page for creating special graphs.

_E_x_a_m_p_l_e_s:

     solids <- list(graph.famous("Tetrahedron"),
                    graph.famous("Cubical"),
                    graph.famous("Octahedron"),
                    graph.famous("Dodecahedron"),
                    graph.famous("Icosahedron"))

