6 problems

For a graph $G$, let $V(G)$ denote its vertex set, let $G\setminus v$ be the graph obtained by deleting $v\in V(G)$, and let $W(G)$ be the Wiener index of $G$. A Šoltés' graph is a…

Let M=(S^3\text{timeshspace{-1.62ex}hspace{-.4ex}hspace{.7ex}}S^1)\#({\mathbb C}{\bf P}^{\,2})^{\# 5}, and let $\text{}^4\hspace{.3pt}15^{\,4}_{\,1}$ denote the specified combi…

Let $G$ be a regular bipartite graph, and let $mbt(G)$ and $\Delta(G)$ denote its maximum book thickness and maximum degree, respectively. Vertex-transitivity conjecture. The count…

An inscribed zonotope is a zonotope whose vertices lie on a common sphere. A zonotope is combinatorially equivalent to another polytope if their face lattices are isomorphic. A…

Let $D_{k,n}$ be the data center network Dcell, with $k\geq0$ and $n\geq2$. Gu et al.'s vertex-transitivity conjecture. $D_{k,n}$ is vertex-transitive for all $k\geq0$ and $n\geq2$…

Grünbaum polyhedron uniqueness conjecture. The Gr"unbaum polyhedron is conjectured to be the only vertex-transitive polyhedron of genus $g\geqslant 2$ that is also combinatorially…