Graphs having extremal monotonic topological indices with bounded vertex k-partiteness

2017/08/03 by Fang Gao, Duo Zhao, Gao, Fang +5 · 1 citation
Chemistry · Computer Science · Mathematics · #05C12 #Combinatorics (math.CO) #F.2.2 #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #Synthesis and Properties of Aromatic Compounds

paper · pdf · doi:10.48550/arxiv.1708.00970

openalex publication_date 2017/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The vertex k-partiteness v_k(G) of graph G is defined as the fewest number of vertices whose deletion from G yields a k-partite graph. In this paper, we introduce two concepts: monotonic decreasing topological index and monotonic increasing topological index, and characterize the extremal graphs having the minimum Wiener index, the maximum Harry index, the maximum reciprocal degree distance, the minimum eccentricity distance sum, the minimum adjacent eccentric distance sum index, the maximum connective eccentricity index, the maximum Zagreb indices among graphs with a fixed number n of vertices and fixed vertex k-partiteness, respectively.

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