20.500.12556/RUL-175449 Vertex partitioning and $p$-energy of graphs For a Hermitian matrix $A$ of order $n$ with eigenvalues $\lambda_1(A)\ge \cdots\ge \lambda_n(A)$, define $\mathcal{E}_p^+(A)=\sum_{\lambda_i > 0} \lambda_i^p(A), \quad \mathcal{E}_p^-(A)=\sum_{\lambda_i<0} |\lambda_i(A)|^p$, to be the positive and the negative $p$-energy of $A$, respectively. In this note, first we show that if $A=[A_{ij}]_{i,j=1}^k$, where $A_{ii}$ are square matrices, then $\mathcal{E}_p^+(A)\geq \sum_{i=1}^{k} \mathcal{E}_p^+(A_{ii}), \quad \mathcal{E}_p^-(A)\geq \sum_{i=1}^{k} \mathcal{E}_p^-(A_{ii})$, for any real number $p\geq 1$. We then apply the previous inequality to establish lower bounds for $p$-energy of the adjacency matrix of graphs. adjacency matrix graph energy positive p-energy negative p-energy Schatten p-norm vertex partition true false true Angleški jezik Angleški jezik Članek v reviji 2025-10-28 09:11:04 2025-10-28 09:11:05 2025-12-11 03:43:36 0000-00-00 00:00:00 2025 0 0 Str. 96-107 Vol. 724 Nov. 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-11-01 519.17 0024-3795 10.1016/j.laa.2025.06.009 241730563 1-s2.0-S0024379525002617-main.pdf 1-s2.0-S0024379525002617-main.pdf 1 7F4FE6885BB645FD88354765C537BDD7 44860c043afd6856c65a514f2de159f40a021ecb68e66721c0fa52138f579a1c 08071750-b3d6-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=220999 https://www.sciencedirect.com/science/article/pii/S0024379525002617 1 5aafd28e-b3d5-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=220997 Fakulteta za matematiko in fiziko 0 0 0