Related papers: The group vertex magicness of unicyclic and bicycl…

In this article, some necessary conditions of group vertex magicness of graphs with at least one pendant, group vertex magicness of product graphs, are proved. A characterization of group vertex magicness of trees of diameter up to 5. for…

In this paper we have discussed the group vertex magicness of H-join of family of graphs and generalized friendship graph.

For a set of distances $D$, a graph $G$ on $n$ vertices is said to be $D$-magic if there exists a bijection $f:V\rightarrow \{1,2, \ldots , n\}$ and a constant $k$ such that for any vertex $x$, $\sum_{y\in N_D(x)} f(y) = k$, where…

Let G be a simple undirected graph and let A be an additive Abelian group with identity 0. In this paper, we introduce the concept of group magic spectrum of a graph G with respect to a given Abelian group A and is defined as spec(G, A):=…

In a graph G, the cardinality of the smallest ordered set of vertices that distinguishes every element of V (G) (resp. E(G)) is called the vertex (resp. edge) metric dimension of G. In [16] it was shown that both vertex and edge metric…

We describe computational results about undirected graphs having $10$ vertices and automorphism group isomorphic to $\mathbb{Z}/4\mathbb{Z}$.

A graph $G = (V, E)$ is called antimagic if there exists a bijective labelling $f : E \rightarrow \{1, 2, \ldots, |E|\}$ such that the vertex-sums of labels over edges incident to a given vertex are all distinct. In this paper, we extend…

An antimagic labelling of a graph $G = (V,E)$ is a bijection from $E$ to $\{1,2, \ldots, |E|\}$, such that all vertex-sums are pairwise distinct, where the vertex-sum of each vertex is the sum of labels over edges incident to this vertex. A…

We describe computational results about undirected graphs having $14$ vertices and automorphism group isomorphic to $\mathbb{Z}/8\mathbb{Z}$, graphs $\Gamma$ which have less than $2|Aut(\Gamma)|$ vertices. We give one example of such…

We show that certain graphs of groups with cyclic edge groups are aTmenable. In particular, this holds when each vertex group is either virtually special or acts properly and semisimply on $\mathbb{H}^n$.

Let $G$ be a finite simple undirected $(p,q)$-graph, with vertex set $V(G)$ and edge set $E(G)$ such that $p=|V(G)|$ and $q=|E(G)|$. A super edge-magic total labeling $f$ of $G$ is a bijection $f\colon V(G)\cup E(G)\longrightarrow…

The metric (resp. edge metric) dimension of a simple connected graph $G$, denoted by dim$(G)$ (resp. edim$(G)$), is the cardinality of a smallest vertex subset $S\subseteq V(G)$ for which every two distinct vertices (resp. edges) in $G$…

A graph $G=(V,E)$ is said to be distance magic if there is a bijection $f$ from a vertex set of $G$ to the first $|V(G)|$ natural numbers such that for each vertex $v$, its weight given by $\sum_{u \in N(v)}f(u)$ is constant, where $N(v)$…

A graph $G$ is called edge-magic if there is a bijective function $f$ from the set of vertices and edges to the set $\{1,2,\ldots,|V(G)|+|E(G)|\}$ such that the sum $f(x)+f(xy)+f(y)$ for any $xy$ in $E(G)$ is constant. Such a function is…

A graph $G=(V,E)$ is antimagic if there is a one-to-one correspondence $f: E \to \{1,2,\ldots, |E|\}$ such that for any two vertices $u,v$, $\sum_{e \in E(u)}f(e) \ne \sum_{e\in E(v)}f(e)$. It is known that bipartite regular graphs are…

A graph is sub-unicyclic if it contains at most one cycle. We also say that a graph $G$ is $k$-apex sub-unicyclic if it can become sub-unicyclic by removing $k$ of its vertices. We identify 29 graphs that are the minor-obstructions of the…

In a graph G, the cardinality of the smallest ordered set of vertices that distinguishes every element of V (G)[E(G) is called the mixed metric dimension of G. In this paper we first establish the exact value of the mixed metric dimension…

For a set of distances $D$, a graph $G$ of order $n$ is said to be $D-$magic if there exists a bijection $f:V\rightarrow \{1,2, \ldots, n\}$ and a constant $k$ such that for any vertex $x$, $\sum_{y\in N_D(x)} f(y) =k$, where…

We associate a graph $\mathcal{C}_G$ to a non locally cyclic group $G$ (called the non-cyclic graph of $G$) as follows: take $G\backslash Cyc(G)$ as vertex set, where $Cyc(G)=\{x\in G | < x,y> \text{is cyclic for all} y\in G\}$ is called…

This article studies a generalization of magic squares to $k$-uniform hypergraphs. In traditional magic squares the entries come from the natural numbers. A magic labeling of the vertices in a graph or hypergraph has since been generalized…