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math.CO2026
Connected graphs minimizing the spectral radius for given order and dissociation number
Zejun Huang, Jiahui Liu, Chenxi Yang
A dissociation set in a graph is a subset of vertices which induces a subgraph with maximum degree at most one. The dissociation number of a graph is the maximum cardinality of its…
math.CO2024
Nonregular graphs with a given maximum degree attaining maximum spectral radius
Zejun Huang, Jiahui Liu, Chenxi Yang
Let be a connected nonregular graphs of order with maximum degree that attains the maximum spectral radius. Liu and Li (2008) proposed a conjecture stating that has…
math.CO2023
Connected graphs with a given dissociation number attaining the minimum spectral radius
Zejun Huang, Jiahui Liu, Xinwei Zhang
A dissociation set of a graph is a set of vertices which induces a subgraph with maximum degree less than or equal to one. The dissociation number of a graph is the maximum cardina…