Table of The Largest Known Graphs of A Given Diameter and Maximal Degree

Table Of The Largest Known Graphs Of A Given Diameter And Maximal Degree

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).

Read more about Table Of The Largest Known Graphs Of A Given Diameter And Maximal Degree:  Table of The Orders of The Largest Known Graphs For The Undirected Degree Diameter Problem

Famous quotes containing the words table of, table, largest and/or degree:

    “Remember thee?
    Ay, thou poor ghost, whiles memory holds a seat
    In this distracted globe. Remember thee?
    Yea, from the table of my memory
    I’ll wipe away all trivial fond records,
    All saws of books, all forms, all pressures past
    That youth and observation copied there,
    And thy commandment all alone shall live
    Within the book and volume of my brain,”
    —William Shakespeare (1564–1616)

    “The gingham dog and the calico cat
    Side by side on the table sat;”
    —Eugene Field (1850–1895)

    “Figure him there, with his scrofulous diseases, with his great greedy heart, and unspeakable chaos of thoughts; stalking mournful as a stranger in this Earth; eagerly devouring what spiritual thing he could come at: school-languages and other merely grammatical stuff, if there were nothing better! The largest soul that was in all England.”
    —Thomas Carlyle (1795–1881)

    “Take but degree away, untune that string,
    And hark what discord follows!
    ...
    Force should be right, or, rather, right and wrong—
    Between whose endless jar justice resides—
    Should lose their names, and so should justice too.
    Then everything includes itself in power,
    Power into will, will into appetite;
    And appetite, an universal wolf,
    So doubly seconded with will and power,
    Must make perforce an universal prey,
    And last eat up himself.”
    —William Shakespeare (1564–1616)