Consider a simple undirected connected graph , with and representing its degree and adjacency matrices, respectively. Furthermore, is the Laplacian matrix of , and is the heat kernel (HK) of , with denoting the time variable. For a vertex , the th element of the diagonal of the HK is defined as , and is the HK trace of , where denote the eigenvalues of . This study provides new computational formulas for the HK diagonal entries of graphs using an almost equitable partition and the Schur complement technique. We also provide bounds for the HK trace of the graphs.
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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC11341236 | PMC |
| http://dx.doi.org/10.1016/j.heliyon.2024.e32235 | DOI Listing |
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