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generalized symmetric distance matrix det

arxiv.org · 299 words · saved by 1 readers

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The additive-multiplicative distance matrix of a graph, and a novel third invariant Graham showed with Pollak and Hoffman-Hosoya that for any directed graph $G$ with strong blocks $G_e$, the determinant $\det(D_G)$ and cofactor-sum $cof(D_G)$ of the distance matrix $D_G$ can be computed from the same quantities for the blocks $G_e$. This was extended to trees - and in our recent work to any graph - with multiplicative and $q$-distance matrices. For trees, we went further and unified all previous variants with weights in a unital commutative ring, into a distance matrix with additive and multi

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