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- W996927351 abstract "Let $A = (a_{i,j})_{1 leq i,j leq n}$ be an $n times n$ matrix where $n geq 2$. Let $det 2(A)$, its second immanant be the immanant corresponding to the partition $lambda_2 = 2,1^{n-2}$. Let $G$ be a connected graph with blocks $B_1, B_2,ldots, B_p$ and with $q$-exponential distance matrix $ED_G$. We give an explicit formula for $det 2(ED_G)$ which shows that $det 2(ED_G)$ is independent of the manner in which $G$'s blocks are connected. Our result is similar in form to the result of Graham, Hoffman and Hosoya and in spirit to that of Bapat, Lal and Pati who show that $det ED_T$ where $T$ is a tree is independent of the structure of $T$ and only dependent on its number of vertices. Our result extends more generally to a product distance matrix associated to a connected graph $G$. Similar results are shown for the $q$-analogue of $T$'s laplacian and a suitably defined matrix for arbitrary connected graphs." @default.
- W996927351 created "2016-06-24" @default.
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- W996927351 date "2015-06-01" @default.
- W996927351 modified "2023-09-23" @default.
- W996927351 title "THE SECOND IMMANANT OF SOME COMBINATORIAL MATRICES" @default.
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- W996927351 doi "https://doi.org/10.22108/toc.2015.6237" @default.
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