𝔖 Bobbio Scriptorium
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On the existence of graphs of diameter two and defect two

✍ Scribed by J. Conde; J. Gimbert


Book ID
108114085
Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
459 KB
Volume
309
Category
Article
ISSN
0012-365X

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πŸ“œ SIMILAR VOLUMES


Reduced graphs of diameter two
✍ Hong-Jian Lai πŸ“‚ Article πŸ“… 1990 πŸ› John Wiley and Sons 🌐 English βš– 444 KB

## Abstract A graph __H__ is __collapsible__ if for every subset X βŠ† __V(H), H__ has a spanning connected subgraph whose set of odd‐degree vertices is X. In any graph __G__ there is a unique collection of maximal collapsible subgraphs, and when all of them are contracted, the resulting contraction

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✍ A. Blokhuis; A. E. Brouwer πŸ“‚ Article πŸ“… 1988 πŸ› Springer 🌐 English βš– 365 KB

We survey what is known on geodetic graphs of diameter two and discuss the implications of a new strong necessary condition for the existence of such graphs.

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A maximal planar graph is a simple planar graph in which every face is a triangle. We show here that such graphs with maximum degree A and diameter two have no more than :A + 1 vertices. We also show that there exist maximal planar graphs with diameter two and exactly LiA + 1 J vertices.

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Skoviera, M., The maximum genus of graphs of diameter two, Discrete Mathematics 87 (1991) 175-180. Let G be a (finite) graph of diameter two. We prove that if G is loopless then it is upper embeddable, i.e. the maximum genus y,&G) equals [fi(G)/Z], where /3(G) = IF(G)1 -IV(G)1 + 1 is the Betti numbe