We introduce a new family of simple graphs, so called, growing graphs. We investigate ways to modify a given simple graph G combinatorially to obtain a growing graph. One may obtain infinitely many growing graphs from a single simple graph. We show that a growing graph obtained from any given simple graph is Cohen–Macaulay and every Cohen–Macaulay chordal graph is a growing graph. We also prove that under certain conditions, a graph is growing if and only if its clique complex is grafted and give several equivalent conditions in this case. Our work is inspired by and generalizes a result of Villarreal on the use of whiskers and the work of Faridi on grafting of simplicial complexes.
@article{10_37236_10908,
author = {Safyan Ahmad and Fazal Abbas and Shamsa Kanwal},
title = {Cohen-Macaulay growing graphs},
journal = {The electronic journal of combinatorics},
year = {2022},
volume = {29},
number = {3},
doi = {10.37236/10908},
zbl = {1502.13028},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10908/}
}
TY - JOUR
AU - Safyan Ahmad
AU - Fazal Abbas
AU - Shamsa Kanwal
TI - Cohen-Macaulay growing graphs
JO - The electronic journal of combinatorics
PY - 2022
VL - 29
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/10908/
DO - 10.37236/10908
ID - 10_37236_10908
ER -
%0 Journal Article
%A Safyan Ahmad
%A Fazal Abbas
%A Shamsa Kanwal
%T Cohen-Macaulay growing graphs
%J The electronic journal of combinatorics
%D 2022
%V 29
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/10908/
%R 10.37236/10908
%F 10_37236_10908
Safyan Ahmad; Fazal Abbas; Shamsa Kanwal. Cohen-Macaulay growing graphs. The electronic journal of combinatorics, Tome 29 (2022) no. 3. doi: 10.37236/10908
