Related papers: A note on distance magic index of partite graphs

In this paper, we determine the distance magic index of lexicograph product of a regular graph with the complement of complete graph, disjoint union of m copies of complete multi- partite graph and disjoint union of m copies of…

In this paper, we provide few results on the group distance magic labeling of lexicographic product and direct product of two graphs. We also prove some necessary conditions for a graph to be group distance magic and provide a…

In this paper, we have studied the distance magic labelling of Generalised Mycielskian of a few families of graphs.

A graph labeling assigns values to the components of a graph (vertices, edges, etc.). In particular, distance magic labelings have been widely studied in undirected graphs. In such a labeling, the vertices are labeled with unique values…

Let $G$ be a complete $k$-partite simple undirected graph with parts of sizes $p_1\le p_2...\le p_k$. Let $P_j=\sum_{i=1}^jp_i$ for $j=1,...,k$. It is conjectured that $G$ has distance magic labeling if and only if $\sum_{i=1}^{P_j}…

A graph $G$ is said to be distance magic if there exists a bijection $f:V\rightarrow \{1,2, \ldots , v\}$ and a constant {\sf k} such that for any vertex $x$, $\sum_{y\in N(x)} f(y) ={\sf k}$, where $N_(x)$ is the set of all neighbours of…

A graph of order $n$ is distance magic if it admits a bijective labeling of its vertices with integers from $1$ to $n$ such that each vertex has the same sum of the labels of its neighbors. In this paper we classify all distance magic…

In this work authors significantly improved previous estimates of the number of edges in subgraphs of the special distance graph.

Let $G=(V,E)$ be a graph of order $n$. A distance magic labeling of $G$ is a bijection $\ell \colon V\rightarrow {1,...,n}$ for which there exists a positive integer $k$ such that $\sum_{x\in N(v)}\ell (x)=k$ for all $v\in V $, where $N(v)$…

In this paper we obtain new estimates of the number of edges in subgraphs of the special distance graph. Bibliography: 21 item.

In this paper, we give a characterization of distance matrices of distance-regular graphs to be invertible.

This paper establishes two techniques to construct larger distance magic and (a, d)-distance antimagic graphs using Harary graphs and provides a solution to the existence of distance magicness of legicographic product and direct product of…

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 $N(v)$…

In this article, the author proposes a new approach for the estimating of the number of edges in induced subgraphs of a special distance graph. Author significantly improves previous estimates and suggests a new approach to obtaining better…

For an arbitrary set of distances $D\subseteq \{0,1, \ldots, d\}$, a graph $G$ is said to be $D$-distance magic if there exists a bijection $f:V\rightarrow \{1,2, \ldots , v\}$ and a constant {\sf k} such that for any vertex $x$,…

Signed graphs have their edges labeled either as positive or negative. Here we introduce two types of signed distance matrix for signed graphs. We characterize balance in signed graphs using these matrices and we obtain explicit formulae…

We introduce the concept of distance ideals of graphs, which can be regarded as a generalization of the Smith normal form and the spectra of the distance matrix of a graph. We obtain a classification of the graphs with at most one trivial…

The Kirchhoff index of a graph is defined as half of the sum of all effective resistance distances between any two vertices. Assuming a complete multipartite graph G, by methods from linear algebra we explicitly formulate effective…

Let $D(G)=(d_{ij})_{n\times n}$ denote the distance matrix of a connected graph $G$ with order $n$, where $d_{ij}$ is equal to the distance between vertices $v_{i}$ and $v_{j}$ in $G$. A graph is called distance integral if all eigenvalues…

A graph is distance magic if it admits a bijective labeling of its vertices by integers from $1$ up to the order of the graph in such a way that the sum of the labels of all the neighbors of a vertex is independent of a given vertex. We…