On the largest A_α-spectral radius of cacti

2018/09/20 by Shaohui Wang, Wang, Shaohui, Chunxiang Wang +5
Chemistry · Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #Synthesis and Properties of Aromatic Compounds

paper · pdf · doi:10.48550/arxiv.1809.07718

openalex publication_date 2018/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A(G) be the adjacent matrix and D(G) the diagonal matrix of the\ndegrees of a graph G, respectively. For 0 \≤ \α \≤ 1, the\nA_\α matrix A_\α(G) = \α D(G) +(1-\α)A(G) is given by\nNikiforov. Clearly, A₀ (G) is the adjacent matrix and 2 A_\(1)/(2)\nis the signless Laplacian matrix. A cactus is a connected graph such that any\ntwo of its cycles have at most one common vertex, that is an extension of the\ntree. The A_\α-spectral radius of a cactus graph with n vertices and\nk cycles is explored. The outcomes obtained in this paper can imply previous\nbounds of Nikiforov et al., and Lov 'asz and Pelik 'an. In addition, the\ncorresponding extremal graphs are determined. Furthermore, we proposed all\neigenvalues of such extremal cacti. Our results extended and enriched previous\nknown results.\n

Citations

• Modern Graph Theory

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