6 problems

Sum-diameter conjecture for paths. For $n\geq 3$, we have

Spum conjecture for paths. For $n\geq 8$, we have

Let $\epsilon(G)$ denote the exclusive sum number of a graph: the least $r$ such that $G$ together with $r$ isolated vertices has an exclusive sum labelling, meaning that the only…

Let $\sigma(G)$ be the sum number of a graph, defined as the smallest number of isolated vertices that can be added to $G$ to obtain a sum graph. A sum graph admits an injective la…

For an integer $k$, obtain a gap-graph of size $k$ from the set $\{2,\ldots,k\}$ by removing one element, called the gap; such a graph has $k-2$ vertices. Let $i$ denote the gap. G…

Let $A_n$ be the graph induced by the relevant labeling construction, let $\mathcal{C}(A_n)$ denote the associated family of graphs, and let a minimal labeling mean a labeling with…