A map is bisingular if each edge is either a loop (This paper only considers planar loop) or an isthmus (i.e., on the boundary of the same face). This paper studies the number of rooted bisingular maps on the sphere a...A map is bisingular if each edge is either a loop (This paper only considers planar loop) or an isthmus (i.e., on the boundary of the same face). This paper studies the number of rooted bisingular maps on the sphere and the torus, and also presents formulae for such maps with three parameters: the root-valency, the number of isthmus, and the number of planar loops.展开更多
It is well known that singular maps(i.e.,those have only one face on a surface)play a key role in the theory of up-embeddability of graphs.In this paper the number of rooted singular maps on the Klein bottle is studie...It is well known that singular maps(i.e.,those have only one face on a surface)play a key role in the theory of up-embeddability of graphs.In this paper the number of rooted singular maps on the Klein bottle is studied.An explicit form of the enumerating function according to the root-valency and the size of the map is determined.Further,an expression of the vertex partition function is also found.展开更多
A map is 4-regular unicursal if all its vertices are 4-valent except two odd-valent vertices. This paper investigates the number of rooted 4-regular unicursal planar maps and presents some formulae for such maps with ...A map is 4-regular unicursal if all its vertices are 4-valent except two odd-valent vertices. This paper investigates the number of rooted 4-regular unicursal planar maps and presents some formulae for such maps with four parameters： the number of edges, the number of inner faces and the valencies of the two odd vertices.展开更多
This paper investigates the number of rooted unicursal planar maps and presents some formulae for such maps with four parameters： the numbers of nonrooted vertices and inner faces and the valencies of two odd vertices.
In this paper a special kind of triangulated maps on the sphere called fair triangulations is enumerated with the size of maps as parameter.Moreover,the number of several other kinds of triangulations are enumerated a...In this paper a special kind of triangulated maps on the sphere called fair triangulations is enumerated with the size of maps as parameter.Moreover,the number of several other kinds of triangulations are enumerated as well.展开更多
This paper provides the parametric expressions satisfied by the enumerating functions for rooted nearly cubic c-nets with the size and/or the root-vertex valency of the maps as the parameters via nonseparable nearly ...This paper provides the parametric expressions satisfied by the enumerating functions for rooted nearly cubic c-nets with the size and/or the root-vertex valency of the maps as the parameters via nonseparable nearly cubic maps. On this basis, two explicit expressions of the functions can be derived by employing Lagrangian inversion.展开更多
基金Supported by fifteenth programming of Central University for Nationalities, NNSFC under Grant No.10271048 and 19831080
文摘A map is bisingular if each edge is either a loop (This paper only considers planar loop) or an isthmus (i.e., on the boundary of the same face). This paper studies the number of rooted bisingular maps on the sphere and the torus, and also presents formulae for such maps with three parameters: the root-valency, the number of isthmus, and the number of planar loops.
基金the National Natural Science Foundation of China(1 983 1 0 80 )
文摘It is well known that singular maps(i.e.,those have only one face on a surface)play a key role in the theory of up-embeddability of graphs.In this paper the number of rooted singular maps on the Klein bottle is studied.An explicit form of the enumerating function according to the root-valency and the size of the map is determined.Further,an expression of the vertex partition function is also found.
基金Supported by the National Natural Science Foundation of China(No.10271017,11371133,11571044)the Natural Science Foundation Project of Chongqing(No.cstc2012jj A00041,cstc2014jcyj A00041)the Innovation Foundation of Chongqing(No.KJTD201321)
文摘A map is 4-regular unicursal if all its vertices are 4-valent except two odd-valent vertices. This paper investigates the number of rooted 4-regular unicursal planar maps and presents some formulae for such maps with four parameters： the number of edges, the number of inner faces and the valencies of the two odd vertices.
基金Supported by the National Natural Science Foundation of China(No.10271017)the Natural Science Foundation Project of Chongqing(N0.cstc2012jjA00041)Chongqing Innovation Fund(grant no.KJTD201321)
文摘This paper investigates the number of rooted unicursal planar maps and presents some formulae for such maps with four parameters： the numbers of nonrooted vertices and inner faces and the valencies of two odd vertices.
基金supported by NSFC(No.10271017)Chongqing Municipal Education Commission (No.KJ101204,No.KJ091217)the Natural Science Foundation Project of Chongqing(No. cstc2012jjA00041)
基金Supported by NSFC(No.10271017,No.11371133)Natural Science Foundation Project of Chongqing(No.cstc2012jjA00041)Chongqing Innovation Fund(No.KJTD201321)
基金This article is supported by National Natural Science Foundation of China (19701002)
文摘In this paper a special kind of triangulated maps on the sphere called fair triangulations is enumerated with the size of maps as parameter.Moreover,the number of several other kinds of triangulations are enumerated as well.
基金This Research is supported by National Natural Science Foundation of China (No. 19831080).
文摘This paper provides the parametric expressions satisfied by the enumerating functions for rooted nearly cubic c-nets with the size and/or the root-vertex valency of the maps as the parameters via nonseparable nearly cubic maps. On this basis, two explicit expressions of the functions can be derived by employing Lagrangian inversion.
