Distinguishing number and distinguishing index of graphs from primary\n subgraphs

2016/07/24 by Samaneh Soltani, Soltani, Samaneh, ‎Saeid Alikhani +1 · 1 citation
Chemistry · Computer Science · Environmental Science · Materials Science · Mathematics · #05C15 #05E18 #Chemistry and Chemical Engineering #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #Photochromic and Fluorescence Chemistry #Various Chemistry Research Topics

paper · pdf · doi:10.48550/arxiv.1607.07084

openalex publication_date 2016/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The distinguishing number (index) D(G) (D'(G)) of a graph G is the\nleast integer d such that G has an vertex labeling (edge labeling) with d\nlabels that is preserved only by a trivial automorphism. Let G be a connected\ngraph constructed from pairwise disjoint connected graphs G₁,\… ,G_k by\nselecting a vertex of G₁, a vertex of G₂, and identify these two\nvertices. Then continue in this manner inductively. We say that G is obtained\nby point-attaching from G₁, \… ,G_k and that G_i's are the primary\nsubgraphs of G. In this paper, we consider some particular cases of these\ngraphs that are of importance in chemistry and study their distinguishing\nnumber and index.\n

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