On the non-existence of antipodal cages of even girth
نویسندگان
چکیده
منابع مشابه
On superconnectivity of (4, g)-cages with even girth
A (k, g)-cage is a k-regular graph with girth g that has the fewest number of vertices. It has been conjectured [Fu, Huang, and Rodger, Connectivity of cages, J. Graph Theory 24 (1997), 187-191] that all (k, g)-cages are k-connected for k ≥ 3. A connected graph G is said to be superconnected if every minimum cut-set S is the neighborhood of a vertex of minimum degree. Moreover, if G − S has pre...
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The well-known Moore bound M(k, g) serves as a universal lower bound for the order of k-regular graphs of girth g. The excess e of a k-regular graph G of girth g and order n is the difference between its order n and the corresponding Moore bound, e = n −M(k, g). We find infinite families of parameters (k, g), g > 6 and even, for which we show that the excess of any k-regular graph of girth g is...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2018
ISSN: 0024-3795
DOI: 10.1016/j.laa.2018.02.010