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Note on Sombor index of connected graphs with given degree sequence
Peichao Wei, Muhuo Liu
For a simple connected graph , let be the degree of the vertex of . The general Sombor index of is defined as $$SO_α(G)=\sum_{uv\in E} \left[d(u)^2+d(v)^…
Extremal problems on planar graphs without k edge-disjoint cycles
Zhai Mingqing, Liu Muhuo
In the 1960s, Erdős and his cooperators initiated the research of the maximum numbers of edges in a graph or a planar graph on vertices without edge-disjoint cycles. This p…
A unified combinatorial view beyond some spectral properties
Xiaofeng Gu, Muhuo Liu
Let . Motivated by jumbled graphs defined by Thomason, the celebrated expander mixing lemma and Haemers's vertex separation inequality, we define that a graph with ver…
The -apex trees with minimum augmented Zagreb index
Muhuo Liu, Shumei Pang, Francesco Belardo +1
For a connected graph on at least three vertices, the augmented Zagreb index (AZI) of is defined as $$AZI(G)=\sum_{uv\in E(G)}\left(\frac{d(u)d(v)}{d(u)+d(v)-2}\right)^{3},…