Staircase graph words
Abstract
Generalizing the notion of staircase words, introduced by Knopfmacher et.\ al, we define staircase graph words. These are functions $w$ from the vertex set $V$ of a graph into the set $\{1,2,\ldots,k\}$, such that $w(x)w(y)\leq 1$, for every adjacent $x,y\in V$. We find the explicit generating functions for the number of staircase graph words for the grid graph, the rectangletriangular graph and the king's graph, all of size $2\times n$.
 Publication:

arXiv eprints
 Pub Date:
 December 2023
 DOI:
 10.48550/arXiv.2312.08273
 arXiv:
 arXiv:2312.08273
 Bibcode:
 2023arXiv231208273F
 Keywords:

 Mathematics  Combinatorics
 EPrint:
 14 pages