8 problems

Goddard–Henning conjecture. If

Let a 2-sphere be a triangulated sphere with $n$ vertices, not necessarily flag, and let $i(\Delta)$ denote its independent domination number, the minimum size of a maximal indepen…

Let $d\geq 2$, and let $G$ be a connected bipartite graph of order $n$. Write $C_{2d+2}$ for the cycle of length $2d+2$, and let $\mathcal{B}_d$ denote the graph family defined in…

Let $d\geq 1$ and let $T$ be a tree of order $n\geq d+1$. The $d$-distance independent domination number $\gamma_d^1(T)$ is the minimum size of a $d$-distance dominating set that i…

Let $G$ be an $r$-regular graph with $r>0$. Let $i(G)$ denote the independent domination number, the minimum cardinality of a maximal independent set, and let $\mu^*(G)$ denote the…

Goddard et al.'s conjecture. If $G$ is a connected bipartite cubic graph that is not $K_{3,3}$, then

Verstraëte's conjecture. If $G$ is a cubic graph with girth at least $6$, then

Let $G$ and $H$ be graphs, and let $i(G)$ denote the smallest cardinality of an independent dominating set in $G$, equivalently the cardinality of a smallest maximal independent se…