The distinguishing number $D(G)$ of a graph $G$ is the least integer $d$ such that $G$ has an vertex labeling with $d$ labels that is preserved only by a trivial automorphism. The minimum size of a label class in such a labeling of $G$ with $D(G) = d$ is called the cost of $d$-distinguishing $G$ and is denoted by $\rho_d(G)$. A set of vertices $S\subseteq V(G)$ is a determining set for $G$ if every automorphism of $G$ is uniquely determined by its action on $S$. The determining number of $G$, ${\rm Det}(G)$, is the minimum cardinality of determining sets of $G$. In this paper we compute the cost and the determining number for the friendship graphs and corona product of two graphs.
Alikhani, S., & Soltani, S. (2021). THE COST NUMBER AND THE DETERMINING NUMBER OF A GRAPH. Journal of Algebraic Systems, 8(2), 209-217. doi: 10.22044/jas.2020.8343.1408
MLA
S. Alikhani; S. Soltani. "THE COST NUMBER AND THE DETERMINING NUMBER OF A GRAPH". Journal of Algebraic Systems, 8, 2, 2021, 209-217. doi: 10.22044/jas.2020.8343.1408
HARVARD
Alikhani, S., Soltani, S. (2021). 'THE COST NUMBER AND THE DETERMINING NUMBER OF A GRAPH', Journal of Algebraic Systems, 8(2), pp. 209-217. doi: 10.22044/jas.2020.8343.1408
VANCOUVER
Alikhani, S., Soltani, S. THE COST NUMBER AND THE DETERMINING NUMBER OF A GRAPH. Journal of Algebraic Systems, 2021; 8(2): 209-217. doi: 10.22044/jas.2020.8343.1408
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