Related papers: On consecutive edge magic total labeling of connec…

An antimagic labeling of a graph $G$ with $m$ edges is a bijection from $E(G)$ to $\{1,2,\ldots,m\}$ such that for all vertices $u$ and $v$, the sum of labels on edges incident to $u$ differs from that for edges incident to $v$. Hartsfield…

An antimagic labeling of a directed graph $D$ with $n$ vertices and $m$ arcs is a bijection from the set of arcs of $D$ to the integers $\{1, \cdots, m\}$ such that all $n$ oriented vertex sums are pairwise distinct, where an oriented…

A strong edge-coloring of a graph $G$ is an assignment of colors to edges such that every color class induces a matching. We here focus on bipartite graphs whose one part is of maximum degree at most $3$ and the other part is of maximum…

Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, and $f$ be a 0-1 labeling of $E(G)$ so that the absolute difference in the number of edges labeled 1 and 0 is no more than one. Call such a labeling $f$ \emph{edge-friendly}.…

Binary classification problems can be naturally modeled as bipartite graphs, where we attempt to classify right nodes based on their left adjacencies. We consider the case of labeled bipartite graphs in which some labels and edges are not…

An antimagic labeling of a directed graph $D$ with $n$ vertices and $m$ arcs is a bijection from the set of arcs of $D$ to the integers $\{1, \cdots, m\}$ such that all $n$ oriented vertex sums are pairwise distinct, where an oriented…

An edge labeling of a graph distinguishes neighbors by sets (multisets, resp.), if for any two adjacent vertices $u$ and $v$ the sets (multisets, resp.) of labels appearing on edges incident to $u$ and $v$ are different. In an analogous way…

A tree $T$ on $2^n$ vertices is called set-sequential if the elements in $V(T)\cup E(T)$ can be labeled with distinct nonzero $(n+1)$-dimensional $01$-vectors such that the vector labeling each edge is the component-wise sum modulo $2$ of…

In 2009, Kong, Wang, and Lee began work on the problem of finding the edge-balanced index sets of complete bipartite graphs $K_{m,n}$ by solving the cases where $n=1$, $2$, $3$, $4$, and $5$, and also the case where $m=n$. In an article…

An {\em antimagic labeling} of a graph with $m$ edges and $n$ vertices is a bijection from the set of edges to the integers $1,...,m$ such that all $n$ vertex sums are pairwise distinct, where a vertex sum is the sum of labels of all edges…

A conjecture of Luo, Tian and Wu (2022) says that for every positive integer $k$ and every finite tree $T$ with bipartition $X$ and $Y$ (denote $t = \max\{|X|,|Y |\})$, every $k$-connected bipartite graph $G$ with $\delta(G) \geq k + t$…

Graph labellings have been a very fruitful area of research in the last four decades. However, despite the staggering number of papers published in the field (over 1000), few general results are available, and most papers deal with…

The concept of graceful labels was proposed by Rosa, scholars began to study graceful labels of various graphs and obtained relevant results.Let the graph is a bipartite graceful graph, we have proved some graphs are graceful labeling in…

A strong edge-coloring $\varphi$ of a graph $G$ assigns colors to edges of $G$ such that $\varphi(e_1)\ne \varphi(e_2)$ whenever $e_1$ and $e_2$ are at distance no more than 1. It is equivalent to a proper vertex coloring of the square of…

The super edge-magicness of graphs of equal order and size has been shown to be important since such graphs can be used as seeds to answer many questions related to (super) edge-magic labelings and other types of well studied labelings, as…

Given a digraph $D$ with $m $ arcs, a bijection $\tau: A(D)\rightarrow \{1, 2, \ldots, m\}$ is an antimagic labeling of $D$ if no two vertices in $D$ have the same vertex-sum, where the vertex-sum of a vertex $u $ in $D$ under $\tau$ is the…

Let $G$ a bipartite graph with vertex bipartition $\{A,B\}$ and let $m=|E(G)|$. An $(A,B)$-uniformly ordered labeling of $G$ is a labeling $f\colon V\rightarrow [0,2m]$ which, among other conditions, requires that there exists $\lambda\in…

Kang and Park recently showed that every cubic (loopless) multigraph is incidence 6-choosable [On incidence choosability of cubic graphs. \emph{arXiv}, April 2018]. Equivalently, every bipartite graph obtained by subdividing once every edge…

A labeling of a digraph $D$ with $m$ arcs is a bijection from the set of arcs of $D$ to $\{1, \ldots, m\}$. A labeling of $D$ is antimagic if no two vertices in $D$ have the same vertex-sum, where the vertex-sum of a vertex $u\in V(D)$ for…

An odd prime labeling is a variation of a prime labeling in which the vertices of a graph of order~$n$ are labeled with the distinct odd integers $1$ to $2n-1$ so that the labels of adjacent vertices are relatively prime. This paper…