4 problems

Let $B_n$ be the book graph with parameter $n$, and let $D(B_n,x)$ denote its domination polynomial. The numerical data suggest the following parity-dependent statement. Real-root…

Let $B_{2,n}$ denote the two-spine book graph with $n$ pages, and let $\operatorname{HGP}(G)$ be the proper hat-guessing number of a graph $G$. Two-spine book graph conjecture. For…

Let $B_{r+1}$ denote the graph consisting of $r+1$ triangles sharing a common edge, and let $\rho(G)$ be the spectral radius of a graph $G$. A graph is $B_{r+1}$-free if it contain…

Let $B_{r+1}$ denote the graph consisting of $r+1$ triangles sharing a common edge, and let $\rho(G)$ be the spectral radius of a graph $G$. A graph is $B_{r+1}$-free if it contain…