3 problems

Modified Ilić and Ilić conjecture. (1) For $G\in\mathcal{U}_{n,l}^g$, if more than two vertices on the cycle have degree at least $3$, then $U^0\preceq G$, with equality if and onl…

Ilić and Ilić's conjecture. Among all $n$-vertex unicyclic graphs, the graph $U_{n,l}^{3,0}$ has the minimum Laplacian coefficients $c_k$, $k=0,\dots,n$; equivalently,…

Let $\pi$ be the degree sequence of a tree, and let … Let $T_{\pi}^*$ denote the tree with degree sequence $\pi$ having minimum Wiener index. Laplacian-coefficient extremal conject…