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- W3205945423 abstract "The QE constant of a finite connected graph $G$, denoted by $mathrm{QEC}(G)$, is by definition the maximum of the quadratic function associated to the distance matrix on a certain sphere of codimension two. We prove that the QE constants of paths $P_n$ form a strictly increasing sequence converging to $-1/2$. Then we formulate the problem of determining all the graphs $G$ satisfying $mathrm{QEC}(P_n)lemathrm{QEC}(G)<mathrm{QEC}(P_{n+1})$. The answer is given for $n=2$ and $n=3$ by exploiting forbidden subgraphs for $mathrm{QEC}(G)<-1/2$ and the explicit QE constants of star products of the complete graphs." @default.
- W3205945423 created "2021-10-25" @default.
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- W3205945423 date "2021-10-16" @default.
- W3205945423 modified "2023-10-10" @default.
- W3205945423 title "Determining finite connected graphs along the quadratic embedding constants of paths" @default.
- W3205945423 doi "https://doi.org/10.5614/ejgta.2021.9.2.23" @default.
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