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Some Properties of Graphs with Multiple Edges
- Source :
- Canadian Journal of Mathematics. 17:166-177
- Publication Year :
- 1965
- Publisher :
- Canadian Mathematical Society, 1965.
-
Abstract
- In this paper we consider undirected graphs, with no edges joining a vertex to itself, but with possibly several edges joining pairs of vertices. The first part of the paper deals with the question of characterizing those sets of non-negative integers d1d2 . . . , dn and {cij}, 1 ≤ i < j ≤ n, such that there exists a graph G with n vertices whose valences (degrees) are the numbers di, and with the additional property that the number of edges joining i and j is at most cij. This problem has been studied extensively, in the general case (1, 2, 9, 11), in the case where the graph is bipartite (3, 5, 7, 10), and in the case where the Cij are all 1 (6).
- Subjects :
- Dense graph
General Mathematics
010102 general mathematics
01 natural sciences
Vertex (geometry)
Combinatorics
Indifference graph
Chordal graph
0103 physical sciences
Bipartite graph
Graph (abstract data type)
010307 mathematical physics
Multiple edges
0101 mathematics
Graph property
Mathematics
Subjects
Details
- ISSN :
- 14964279 and 0008414X
- Volume :
- 17
- Database :
- OpenAIRE
- Journal :
- Canadian Journal of Mathematics
- Accession number :
- edsair.doi...........5164a36c485369705de0ffdb6c239cbb