Related papers: Lattice Grids and Prisms are Antimagic

The anti-forcing number of a perfect matching $M$ of a graph $G$ is the minimal number of edges not in $M$ whose removal to make $M$ as a unique perfect matching of the resulting graph. The set of anti-forcing numbers of all perfect…

We introduce and study the problem of constructing geometric graphs that have few vertices and edges and that are universal for planar graphs or for some sub-class of planar graphs; a geometric graph is \emph{universal} for a class…

Let $G = (V,E)$ be a connected simple graph. A bijection $f: E \rightarrow \{1,2,\ldots,|E|\}$ is called a local antimagic labeling of $G$ if $f^+(u) \neq f^+(v)$ holds for any two adjacent vertices $u$ and $v$, where $f^+(u) = \sum_{e\in…

Let $G = (V, E)$ be a finite simple undirected graph without $K_2$ components. A bijection $f : E \rightarrow \{1, 2,\cdots, |E|\}$ is called a local antimagic labeling if for any two adjacent vertices $u$ and $v$, they have different…

Call a colouring of a graph \emph{distinguishing} if the only automorphism of this graph which preserves said colouring is the identity. Let $H$ be an arbitrary graph. We say that a graph $G$ is \emph{$H$-free} if $G$ does not contain an…

A simple and connected $n$-vertex graph has a prime vertex labeling if the vertices can be injectively labeled with the integers $1, 2, 3,\ldots, n$, such that adjacent vertices have relatively prime labels. We will present previously…

A bijective mapping $f: V(G) \rightarrow \left\{1,2,\ldots,n\right\}$ is called a \emph{Distance Magic Labeling (DML) of $G$} if ~ ${\sum_{v \in N(u)}} f(v) $ is a constant for all $u\in V(G)$ where $G$ is a simple graph of order $n$ and…

A graph $G$ is called \emph{symmetric with respect to a functional $F_G(P)$} defined on the set of all the probability distributions on its vertex set if the distribution $P^*$ maximizing $F_G(P)$ is uniform on $V(G)$. Using the…

The $k$-coprime graph of order $n$ is the graph with vertex set $\{k, k+1, \ldots, k+n-1\}$ in which two vertices are adjacent if and only if they are coprime. We characterize Hamiltonian $k$-coprime graphs. As a particular case, two…

An edge labeling of a graph $G = (V, E)$ is said to be local antimagic if it is a bijection $f:E \to\{1,\ldots ,|E|\}$ such that for any pair of adjacent vertices $x$ and $y$, $f^+(x)\not= f^+(y)$, where the induced vertex label of $x$ is…

A graph $G$ is said to be perfectly divisible if for every induced subgraph $H$ of $G$ with at least one edge, the vertex set $V(H)$ can be partitioned into two sets $A, B$ such that $H[A]$ is perfect and $\omega(B) < \omega(H)$. It is easy…

A labelling of a graph is an assignment of labels to its vertex or edge sets (or both), subject to certain conditions, a well established concept. A labelling of a graph G of order n is termed a numbering when the set of integers {1,...,n}…

A total prime labeling of a graph of order $n$ is an extension of a prime labeling in which we distinctly label the vertices and edges. The goal of the labeling is for adjacent vertex labels to be relatively prime, and for each vertex of…

A symmetric $m\times m$ matrix $M$ with entries taken from $\{0,1,\ast\}$ gives rise to a graph partition problem, asking whether a graph can be partitioned into $m$ vertex sets matched to the rows (and corresponding columns) of $M$ such…

A $\Gamma$-distance magic labeling of a graph $G=(V,E)$ with $|V | = n$ is a bijection $\ell$ from $V$ to an Abelian group $\Gamma$ of order $n$ such that the weight $w(x)=\sum_{y\in N_G(x)}\ell(y)$ of every vertex $x \in V$ is equal to the…

An edge of a graph of order $n$ is pancyclic if it lies in a cycle of every length $3,\ldots,n$. A graph of order $n$ is vertex-pancyclic if every vertex lies in a cycle of every length $3,\ldots,n$. Recently, Li and Zhan proved that every…

An \emph{antilattice} is an algebraic structure based on the same set of axioms as a lattice except that the two commutativity axioms for $\land$ and $\lor$ are replaced by anticommutative counterparts. In this paper we study certain…

Let $G=(V, E)$ be a connected graph. A bijection $f: E\to \{1, \ldots, |E|\}$ is called a local antimagic labeling if for any two adjacent vertices $x$ and $y$, $f^+(x)\neq f^+(y)$, where $f^+(x)=\sum_{e\in E(x)}f(e)$ and $E(x)$ is the set…

A graph is called a sum graph if its vertices can be labelled by distinct positive integers such that there is an edge between two vertices if and only if the sum of their labels is the label of another vertex of the graph. Most papers on…

Let G=(V(G),E(G)) be a connected simple graph with n vertices and m edges. A bijection f from the edge set of G to [m] is called a local antimagic labeling of G, if for any two adjacent vertices u and v in G, the sums of the weights of the…