Related papers: $m$-Magic Labeling on Anti Fuzzy Path Graph
We enumerate factorisations of the complete bipartite graph into spanning semiregular graphs in several cases, including when the degrees of all the factors except one or two are small. The resulting asymptotic behaviour is seen to…
We study the eternal dominating number and the m-eternal dominating number on digraphs. We generalize known results on graphs to digraphs. We also consider the problem "oriented (m-)eternal domination", consisting in finding an orientation…
Our aim in this paper is to introduce the relatively new concept of *-density of a fuzzy graph and *-balanced fuzzy graph. Several examples and results are also provided. In addition, many operations on fuzzy graphs that preserves…
In order to apply canonical labelling of graphs and isomorphism checking in interactive theorem provers, these checking algorithms must either be mechanically verified or their results must be verifiable by independent checkers. We analyze…
Many signals on Cartesian product graphs appear in the real world, such as digital images, sensor observation time series, and movie ratings on Netflix. These signals are "multi-dimensional" and have directional characteristics along each…
We show that there exists an adjacency labelling scheme for planar graphs where each vertex of an $n$-vertex planar graph $G$ is assigned a $(1+o(1))\log_2 n$-bit label and the labels of two vertices $u$ and $v$ are sufficient to determine…
Many problems can be presented in an abstract form through a wide range of binary objects and relations which are defined over problem domain. In these problems, graphical demonstration of defined binary objects and solutions is the most…
For a flexible labeling of a graph, it is possible to construct infinitely many non-equivalent realizations keeping the distances of connected points constant. We give a combinatorial characterization of graphs that have flexible labelings.…
This paper studies the hypothesis testing problem to determine whether m > 2 unlabeled graphs with Gaussian edge weights are correlated under a latent permutation. Previously, a sharp detection threshold for the correlation parameter \rho…
Assume that there is a free group action of automorphisms on a bipartite graph. If there is a perfect matching on the factor graph, then obviously there is a perfect matching on the graph. Surprisingly, the reversed is also true for…
To investigate hyperbinary expansions of a nonnegative integer~$n$, an edge-labeled directed graph $A(n)$ has recently been introduced. After pointing out some new simple facts about its cyclomatic number, we give a relatively simple…
Given a graph $G=(V,E)$ and a colouring $f:E\mapsto \mathbb N$, the induced colour of a vertex $v$ is the sum of the colours at the edges incident with $v$. If all the induced colours of vertices of $G$ are distinct, the colouring is called…
A bijective function $f:V\rightarrow\left\{1,2,3,...,|V| \right\}$ is said to be a local distance antimagic labeling of a graph $G=(V,E)$, if $w(u)\neq w(v)$ for any two adjacent vertices $u, v$ where the weight $w(v)=\sum_{z\in N(v)}f(z)$.…
This paper shows that the endograph metric and the $\Gamma$-convergence are compatible on a large class of fuzzy set in $\mathbb{R}^m$.
This book, in order to generalize the two models of fuzzy cognitive maps and neutrosophic cognitive maps, has systematically invented mathematical tools like bimatrices, trimatrices, n-matrices, bigraphs, trigraphs and n-graphs and describe…
The enormous amount of data to be represented using large graphs exceeds in some cases the resources of a conventional computer. Edges in particular can take up a considerable amount of memory as compared to the number of nodes. However,…
Graph symmetries intervene in diverse applications, from enumeration, to graph structure compression, to the discovery of graph dynamics (e.g., node arrival order inference). Whereas Erd\H{o}s-R\'enyi graphs are typically asymmetric, real…
A graph $G$ is said to be super edge-magic if there exists a bijective function $f:V\left(G\right) \cup E\left(G\right)\rightarrow \left\{1, 2, \ldots , \left\vert V\left( G\right) \right\vert +\left\vert E\left( G\right) \right\vert…
In this paper we define some new labellings for trees, called the in-improper and out-improper odd-graceful labellings such that some trees labelled with the new labellings can induce graceful graphs having at least a cycle. We, next, apply…
Let $N_{\mathcal{P}}(n,H)$ denote the maximum number of copies of $H$ in an $n$ vertex planar graph. The problem of bounding this function for various graphs $H$ has been extensively studied since the 70's. A special case that received a…