7 problems

Let $G$ be a graph with $k$ pendant edges, let $\Delta(G)$ be its maximum degree, and let $\chi_{lt}(G)$ denote its local total antimagic chromatic number. Local total antimagic bo…

Let $T$ be a complete full $t$-ary tree, meaning a rooted tree in which every nonleaf has exactly $t$ children and all leaves have the same depth. Let $l$ be the number of leaves a…

Let $G$ be a graph and let $t$ be a positive integer. Write $G\cup tP_3$ for the disjoint union of $G$ and $t$ copies of $P_3$, and let $\tau(G)$ be the maximum integer such that…

Let $T$ be a caterpillar, and let $G$ be a subdivided caterpillar, meaning a subdivision of $T$ in which all edges of $T$ that are not on the central path of $T$ are subdivided the…

Let $G$ be a graph, and let $k$ be an integer. A $k$-shifted-antimagic labeling of $G$ is an injective edge labeling by the consecutive integers $k+1,k+2,\ldots,k+|E(G)|$ such that…

Let $G$ be a graph with $m$ edges and no isolated edge. For each vertex $v$, let $S_v$ be the sum of the labels on edges incident with $v$. A distance-two antimagic labelling uses…

Liang's conjecture. If every node in $S$ has degree at most $4$ and every node in $T$ has degree at most $3$, then $G$ has a matching $M$ and a family $\mathcal{F}$ of node-disjoin…