TY - JOUR
ID - 101675
TI - The Distinguishing Number and the Distinguishing Index of Graphs from Primary Subgraphs
JO - Iranian Journal of Mathematical Chemistry
JA - IJMC
LA - en
SN - 2228-6489
AU - Alikhani, Saeid
AU - Soltani, Samaneh
AD - Yazd University, Yazd, Iran
AD - Department of Mathematics, Yazd University, 89195-741, Yazd, Iran
Y1 - 2019
PY - 2019
VL - 10
IS - 3
SP - 223
EP - 240
KW - Distinguishing index
KW - distinguishing number
KW - Chain
KW - Link
DO - 10.22052/ijmc.2019.152413.1400
N2 - The distinguishing number (index) D(G) (D'(G)) of a graph G is the least integer d such that G has an vertex labeling (edge labeling) with d labels that is preserved only by a trivial automorphism. Let G be a connected graph constructed from pairwise disjoint connected graphs G1,... ,Gk by selecting a vertex of G1, a vertex of G2, and identifying these two vertices. Then continue in this manner inductively. We say that G is obtained by point-attaching from G1, ... ,Gk and that Gi's are the primary subgraphs of G. In this paper, we consider some particular cases of these graphs that are of importance in chemistry and study their distinguishing number and distinguishing index.
UR - https://ijmc.kashanu.ac.ir/article_101675.html
L1 - https://ijmc.kashanu.ac.ir/article_101675_e08d1f5689447168e1f75217e9827f63.pdf
ER -