I found two different definitions of the Moebius Ladder Graph, whose essential difference is, whether the smallest one shall be $K\_4$ or $K\_{3,3}$. 


according to Wikipedia (<http://en.wikipedia.org/wiki/M%C3%B6bius_ladder>),  

"*In graph theory, the Möbius ladder Mn is a cubic circulant graph with an even number n of vertices, formed from an n-cycle by adding edges (called "rungs") connecting opposite pairs of vertices in the cycle*".  

that definition would cover $K\_4$ as a Moebius Ladder.


according to Wolfram's Mathworld (<http://mathworld.wolfram.com/MoebiusLadder.html>), however
"*A Möbius ladder, sometimes called a Möbius wheel (Jakobson and Rivin 1999), of order n is a simple graph obtained by introducing a twist in a prism graph of order n that is isomorphic to the circulant graph $Ci\_{2n}(1,n)$.*" and, because an n-Prism graph has $2n$ vertices and $3n$ edges, that would imply, that the smallest Moebius Ladder graph is $K\_{3,3}$ and not $K\_4$. 


The "dispute" reminds me somehow of the "*is 1 a prime number*" topic and **I would therefore like to know**, if there are mathematical reasons in favor or against either of the definitions (I would however not count the analogy to the one-sided Moebius surface as sufficient justification).



Definition of the Moebius Ladder Graph
As far as I can see, the *intent* of both definitions is to give a description of the Moebius ladder as the circulant on $2n$ vertices with connection set $\{\pm 1, n\}$ which clearly includes $K\_4$.


The "verbose" definition, as a prism with a twist etc. just seems to be wrong, basically because the first half of the definition contradicts the second. In this case, I'll go with the formal mathematical definition rather than the verbal part.


My graph-theorist's opinion: Smallest Moebius ladder is unambiguously $K\_4$.


My matroid-theorist's opinion: Smallest Moebius ladder is *actually* $3K\_2$ the graph with a triple edge connecting two vertices (i.e. the circulant with connection set +1, -1 and 1)


