Even graphs


Göbel, F. and Veldman, H.J. (1986) Even graphs. Journal of Graph Theory, 10 (2). pp. 225-239. ISSN 0364-9024

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Abstract:A nontrivial connected graph G is called even if for each vertex v of G there is a unique vertex [bar v] such that d(v,[bar v]) = diam G. Special classes of even graphs are defined and compared to each other. In particular, an even graph G is called symmetric if d(u,v) + d(u,[bar v]) = diam G for all u, v V(G). Several properties of even and symmetric even graphs are stated. For an even graph of order n and diameter d other than an even cycle it is shown that n ≥ 3d - 1 and conjectured that n ≥ 4d - 4. This conjecture is proved for symmetric even graphs and it is shown that for each pair of integers n, d with n even, d ≥ 2 and n ≥ 4d - 4 there exists an even graph of order n and diameter d. Several ways of constructing new even graphs from known ones are presented.
Item Type:Article
Copyright:© 1986 Wiley InterScience
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/70817
Official URL:https://doi.org/10.1002/jgt.3190100212
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