The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.



Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A159191 Number of n-colorings of the Robertson graph. 2
0, 0, 0, 24, 3490848, 3501104400, 564523119840, 31643453033640, 886834653776064, 15220684846368288, 181298924180884800, 1627952400490177080, 11672280987833510880, 69664869701930893104, 357038627052783076128, 1609181428647593728200, 6498071673405936462720 (list; graph; refs; listen; history; text; internal format)



The Robertson graph is the unique (4,5) cage: the quartic graph on 19 vertices (so 38 edges) with girth 5.


Alois P. Heinz, Table of n, a(n) for n = 0..1000

Weisstein, Eric W. "Robertson Graph".

Weisstein, Eric W. "Chromatic Polynomial".

Timme, Marc; van Bussel, Frank; Fliegner, Denny; Stolzenberg, Sebastian (2009) "Counting complex disordered states by efficient pattern matching: chromatic polynomials and Potts partition functions", New J. Phys. 11 023001, doi: 10.1088/1367-2630/11/2/023001.


a(n) = n^19 -38*n^18 + ... (see Maple program).


a:= n-> n^19 -38*n^18 +703*n^17 -8436*n^16 +73761*n^15 -500004*n^14 +2727105*n^13 -12246808*n^12 +45913333*n^11 -144701057*n^10 +383839223*n^9 -853388854*n^8 +1574465385*n^7 -2370057775*n^6 +2835163369*n^5 -2587310804*n^4 +1685281636*n^3 -693467820*n^2 +134217080*n:

seq(a(n), n=0..20);


The adjacency lists of the Robertson graph are included in A184945.

Cf. A115400, A140986, A157959, A157991, A157992, A157993, A158343, A158344, A158346, A158347, A158348, A158760, A158792, A158904, A159042, A159055, A159056, A159192, A159299, A166964, A173705, A173710.

Sequence in context: A319977 A268505 A172734 * A013820 A294326 A255322

Adjacent sequences:  A159188 A159189 A159190 * A159192 A159193 A159194




Alois P. Heinz, Apr 05 2009



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 2 22:46 EST 2021. Contains 349445 sequences. (Running on oeis4.)