4 problems

Let $n$ be the order of a graph, and let a circulant graph be a graph whose vertices and adjacency relation are invariant under cyclic translation. Let $\operatorname{mp}(G)$ denot…

Let a $(d,g)$-cage $G$ be a graph of degree $d$ and girth $g$, and let $\operatorname{mp}(G)$ denote its monophonic position number. Thomas's conjecture. For sufficiently large $g$…

Let $G$ be a cubic graph of order $n$, and let $\operatorname{mp}(G)$ denote its monophonic position number. Thomas's conjecture. The largest possible monophonic position number of…

A $(d,g)$-cage is a graph of minimum possible order among graphs with degree $d$ and girth $g$, and ${\rm mp}(G)$ denotes the monophonic position number of $G$. The cage monophonic…