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- W1504204633 abstract "Let $G$ be a simple graph with no even cycle, called an odd-cycle graph. Cavers et al. [Linear Algebra Appl. 436(12):4512-1829, 2012] showed that the spectral radius of $G^sigma$ is the same for every orientation $sigma$ of $G$, and equals the maximum matching root of $G$. They proposed a conjecture that the graphs which attain the maximum skew spectral radius among the odd-cycle graphs $G$ of order $n$ are isomorphic to the odd-cycle graph with one vertex degree $n-1$ and size $m=lfloor 3(n-1)/2rfloor$. By using the Kelmans transformation, we give a proof to the conjecture. Moreover, sharp upper bounds of the maximum matching roots of the odd-cycle graphs with given order $n$ and size $m$ are given and extremal graphs are characterized." @default.
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- W1504204633 date "2015-03-23" @default.
- W1504204633 modified "2023-09-24" @default.
- W1504204633 title "Solution to a Conjecture on the Maximum Skew-Spectral Radius of Odd-Cycle Graphs" @default.
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- W1504204633 doi "https://doi.org/10.37236/4919" @default.
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