  The total chromatic number conjecture which has appeared in a few hundred
articles and in numerous books thus far is now one of the classic mathematical
unsolved problems. It appears that many authors coincidentally have attributed
it to Professor M. Behzad and/or to Professor V. G. Vizing. Eventually after
four decades, Professor A. Soifer investigated the origin of this conjecture;
published his findings in The Mathematical Coloring Book - 2009; and stated
that, "In my opinion this unquestionably merits the joint credit to Vizing and
Behzad." After checking all the arguments presented and the blames cited, I
decided to investigate the controversy stated in this book on my own. My
findings which are presented in this report specifically signify the following
two points. - M. Behzad is the sole author of the Total Chromatic Number
Conjecture. - The wrong referrals provided by numerous authors over the last
forty four years, to indicate Vizing's authorship, must be brought to the
attention of the authors and researchers, by appropriate means, as soon as
possible.
