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A Note on Primitive Graphs

Published online by Cambridge University Press:  20 November 2018

I. Z. Bouwer  and
G. F. LeBlanc
I. Z. Bouwer
Affiliation:
University of New Brunswick, Fredericton, New Brunswick
G. F. LeBlanc
Affiliation:
University of New Brunswick, Fredericton, New Brunswick
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Let G denote a connected graph with vertex set V(G) and edge set E(G). A subset C of E(G) is called a cutset of G if the graph with vertex set V(G) and edge set E(G)—C is not connected, and C is minimal with respect to this property. A cutset C of G is simple if no two edges of C have a common vertex. The graph G is called primitive if G has no simple cutset but every proper connected subgraph of G with at least one edge has a simple cutset. For any edge e of G, let G—e denote the graph with vertex set V(G) and with edge set E(G)—e.

Type
Mathematical Notes
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 3 , September 1972 , pp. 437 - 440
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Graham, R. L., On primitive graphs and optimal vertex assignments, Proc. Internat. Conf. on Combinatorial Mathematics, New York, April 1970; New York Academy of Sciences, 1970.Google Scholar
2. Seshu, S. and Reed, M., Linear graphs and electrical networks, Addison-Wesley, Reading, Mass. 1961.Google Scholar