Table of the largest known graphs of a given diameter and maximal degree information
In graph theory, the degree diameter problem is the problem of finding the largest possible graph for a given maximum degree and diameter. The Moore bound sets limits on this, but for many years mathematicians in the field have been interested in a more precise answer. The table below gives current progress on this problem (excluding the case of degree 2, where the largest graphs are cycles with an odd number of vertices).
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In graph theory, thedegreediameter problem is the problem of finding thelargest possible graph for agiven maximum degreeanddiameter. The Moore bound...
triangular number), and is a regular graphofdegree n – 1. All complete graphs are their own maximal cliques. They are maximally connected as the only vertex...
containing the complete graph K4 (such a characterisation is known for K4-free planar graphs) Classify graphs with representation number 3, that is, graphs that...
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being a finite union of algebraic varieties, its dimension is the maximum ofthe dimensions of its components. It is equal to themaximal length ofthe chains...
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the Snake-in-the-box problem and on the Graceful labeling ofgraphs. One of Hunter's conjectures (1999) became known as Snevily's Conjecture: Given an...
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the PVF. The WMAP team finds that the PVF is greater than half of its maximal value (the "full width at half maximum", or FWHM) over an interval of 115...
lower and is determined by thediameterofthe tubes anddegreeof nesting, compared with a surface area of about 3000 m2/g of activated carbons. Nevertheless...
occurred in the force-frequency response ofthe soleus in the flight animals, suggesting a switch to a faster contractile phenotype. Maximal shortening...
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