Robertson–Wegner graph

5-regular undirected graph with 30 vertices and 75 edges
Robertson–Wegner graph
Named afterNeil Robertson
Vertices30
Edges75
Radius3
Diameter3
Girth5
Automorphisms20
Chromatic number4
Chromatic index5[1]
PropertiesCage
Table of graphs and parameters

In the mathematical field of graph theory, the Robertson–Wegner graph is a 5-regular undirected graph with 30 vertices and 75 edges named after Neil Robertson and Gerd Wegner.[2][3][4]

It is one of the four (5,5)-cage graphs, the others being the Foster cage, the Meringer graph, and the Wong graph.

It has chromatic number 4, diameter 3, and is 5-vertex-connected.

Algebraic properties

The characteristic polynomial of the Robertson–Wegner graph is

( x − 5 ) ( x − 2 ) 8 ( x + 1 ) ( x + 3 ) 4 ( x 4 + 2 x 3 − 4 x 2 − 5 x + 5 ) 2 ( x 4 + 2 x 3 − 6 x 2 − 7 x + 11 ) 2 . {\displaystyle (x-5)(x-2)^{8}(x+1)(x+3)^{4}(x^{4}+2x^{3}-4x^{2}-5x+5)^{2}(x^{4}+2x^{3}-6x^{2}-7x+11)^{2}.}

References

  1. ^ Weisstein, Eric W. "Class 2 Graph". MathWorld.
  2. ^ Weisstein, Eric W. "Robertson–Wegner Graph". MathWorld.
  3. ^ Bondy, J. A. and Murty, U. S. R. Graph Theory with Applications. New York: North Holland, p. 238, 1976.
  4. ^ Wong, P. K. "A note on a paper of G. Wegner", Journal of Combinatorial Theory, Series B, 22:3, June 1977, pgs 302-303, doi:10.1016/0095-8956(77)90081-8