2025/01/10 by Shrabani Das, Das, Shrabani, Ahmad Erfanian +3
Chemistry · Mathematics · #FOS: Mathematics #Graph theory and applications #Group Theory (math.GR) #History and advancements in chemistry #Molecular spectroscopy and chirality
paper · pdf · doi:10.48550/arxiv.2501.06124
openalex publication_date 2025/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a group and L(G) be the set of all subgroups of G. The subgroup generating bipartite graph B(G) defined on G is a bipartite graph whose vertex set is partitioned into two sets G × G and L(G), and two vertices (a, b) ∈ G × G and H ∈ L(G) are adjacent if H is generated by a and b. In this paper, we deduce expressions for first and second Zagreb indices of B(G) and obtain a condition such that B(G) satisfy Hansen-Vukičević conjecture [Hansen, P. and Vukičević, D. Comparing the Zagreb indices, \em Croatica Chemica Acta, 80(2), 165-168, 2007]. It is shown that B(G) satisfies Hansen-Vukičević conjecture if G is a cyclic group of order 2p, 2p2, 4p, 4p2 and pn; dihedral group of order 2p and 2p2; and dicyclic group of order 4p and 4p2 for any prime p. While computing Zagreb indices of B(G) we have computed °B(G)(H) for all H ∈ L(G) for the above mentioned groups. Using these information we also compute Randic Connectivity index, Atom-Bond Connectivity index, Geometric-Arithmetic index, Harmonic index and Sum-Connectivity index of B(G).