Paper Info
Title
Edge-oblique polyhedral graphs
Abstract
Extended Abstract By we denote the set of polyhedral graphs, and let G = G ( V , E , F ) ∈ .The degree d(x) of a vertex × ∈ V(G) is the number of edges incident with x . The degree d(α) of a face α ∈ F(G) is the number of edges incident with α . e = ( x , y ; α , β ) ∈ E ( G ) denotes an edge incident with the two vertices x, y ∈ V(G), d(x) ≤ d(y) and incident with the two faces α , β ∈ F ( G ), d ( α ) ≤ d ( β ). [ K = d ( x ) ≤ d ( y ); M = d ( α ), N = d ( β )] is the type of e = ( x , y ; α , β ). S.Jendrol & M.Tkac. [1,2] described all polyhedral graphs having only one or exactly two types of edges. Δ( G ) := max{ d ( a ) : a ∈ V ∪ F } is the maximum degree of G . Because G is a polyhedral graph there is no edge of type (3, 3; 3, 3} in G except G is the tetrahedron . On the 9. High Tatra Conference on Colourings and Cycles in 2000 P.Owens asked the following question: Let k,l be two integers with 1 ≤ l ≤ k. Does there exist a polyhedral graph G with k = ∣E(G)∣ edges and l different types of edges? The cases l ∈ {1,2} are solved in [2]. In this paper we are interested in the case k = l . G is called to be edge –; oblique if for any type of edges there is at most one edge in E(G) having this type
Year
DOI
Venue
2004
10.1016/S0166-218X(03)00447-5
Electronic Notes in Discrete Mathematics
Keywords
Field
DocType
finite number,maximum degree,common edge-type,polyhedral graph,z-edge-oblique graph,edge incident,edge-oblique polyhedral graph,optimization,polyhedron,vertex graph
Discrete mathematics,Graph,Combinatorics,Oblique case,Finite set,Vertex (geometry),Vertex (graph theory),Polyhedron,Polyhedral graph,Degree (graph theory),Mathematics
Journal
Volume
Issue
ISSN
136
2-3
Discrete Applied Mathematics
Citations 
PageRank 
References 
1
0.47
4
Authors
2
Name
Order
Citations
PageRank
Jens Schreyer1164.17
Hansjoachim Walther29720.10