| Two Types of Planar Graphs in Which Group Operations Can Be Introduced |
| Received:May 29, 1982 Revised:October 30, 1985 |
| Key Words:
|
| Fund Project: |
|
| Hits: 1947 |
| Download times: 1165 |
| Abstract: |
| A planar graph G is called an In-gragh if the degree of every its interior vertex is an integer times n. In this paper we establish corresponding relations between degrees of vertices of the I2 or I3-graph and elements of the symmetric group Φ3 of degree 3 or the alternating group Ψ4 of degree 4. Moreover, we prove that for a hole-discrete I2 or I3-graph G, the product of the group's elements corresponding to the vertices of every hole is the unit elemente, iff V(G) is 3-colorable or orderedly 4-colorable.On these grounds, we find some regularities on degrees of vertices of these planar graphs, and solve a question on existence of planar graphs with some prescribed types of vertices and faces. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.1986.01.043 |
| View Full Text View/Add Comment |
