Related papers: A Study on the Product Set-Labeling of Graphs

A signed graph is a graph with edges marked positive and negative; it is unbalanced if some cycle has negative sign product. We introduce the concept of vector valued switching function in signed graphs, which extends the concept of…

A graph $G(V,E)$ is $\Gamma$-harmonious when there is an injection $f$ from $V$ to an Abelian group $\Gamma$ such that the induced edge labels defined as $w(xy)=f(x)+f(y)$ form a bijection from $E$ to $\Gamma$. We study $\Gamma$-harmonious…

An {\em arrangement} of an ordered pair $(G_A, G_M)$ of graphs is defined as a function $f$ from $V(G_A)$ to $V(G_M)$ such that, for each vertex $c$ of $G_M$, the vertex-set $f^{-1}(c)$ of $G_A$ either is $\emptyset$ (the case when $c…

The F-index of a graph $G$ is the sum of the cubes of the degrees of the vertices of $G$. In this paper, explicit expressions for the F-index of different transformation graphs of type ${{G}^{xyz}}$ with $x, y, z\in \{-, + \}$ are obtained.…

Domination in graphs is a widely studied field, where many different definitions have been introduced in the last years to respond to different network requirements. This paper presents a new dominating parameter based on the well-known…

Graph signal processing represents an important advancement in the field of data analysis, extending conventional signal processing methodologies to complex networks and thereby facilitating the exploration of informative patterns and…

A graph composition is a partition of the vertex set such that each member of the partition induces a connected sub- graph, and the composition number of a graph is the number of possible graph compositions. A partition of a set S of…

A colouring of a graph $G=(V,E)$ is a function $c: V\rightarrow\{1,2,\ldots \}$ such that $c(u)\neq c(v)$ for every $uv\in E$. A $k$-regular list assignment of $G$ is a function $L$ with domain $V$ such that for every $u\in V$, $L(u)$ is a…

Graph representation learning (also called graph embeddings) is a popular technique for incorporating network structure into machine learning models. Unsupervised graph embedding methods aim to capture graph structure by learning a…

Graph representation learning is a fundamental research issue in various domains of applications, of which the inductive learning problem is particularly challenging as it requires models to generalize to unseen graph structures during…

In this paper, we consider two ways of breaking a graph's symmetry: distinguishing labelings and fixing sets. A distinguishing labeling $\phi$ of $G$ colors the vertices of $G$ so that the only automorphism of the labeled graph $(G, \phi)$…

Let $G=(V,E,w)$ be a finite, connected graph with weighted edges. We are interested in the problem of finding a subset $W \subset V$ of vertices and weights $a_w$ such that $$ \frac{1}{|V|}\sum_{v \in V}^{}{f(v)} \sim \sum_{w \in W}{a_w…

Finding densely connected groups of nodes in networks is a widely used tool for analysis in graph mining. A popular choice for finding such groups is to find subgraphs with a high average degree. While useful, interpreting such subgraphs…

Node classification is the task of predicting the labels of unlabeled nodes in a graph. State-of-the-art methods based on graph neural networks achieve excellent performance when all labels are available during training. But in real-life,…

A broadcast on a graph $G=(V,E)$ is a function $f: V\longrightarrow \{0,\ldots,\operatorname{diam}(G)\}$ such that $f(v)\leq e\_G(v)$ for every vertex $v\in V$, where$\operatorname{diam}(G)$ denotes the diameter of $G$ and $e\_G(v)$ the…

Given a graph $G=(V,E)$, and a function $f:V(G) \rightarrow \mathbb{N}$, an $f$-reversible process on $G$ is a dynamical system such that, given an initial vertex labeling $c_0 : V(G) \rightarrow \{0,1\}$, every vertex $v$ changes its label…

Graphical tensor notation is a simple way of denoting linear operations on tensors, originating from physics. Modern deep learning consists almost entirely of operations on or between tensors, so easily understanding tensor operations is…

Rapidly shrinking technology node and voltage scaling increase the susceptibility of Soft Errors in digital circuits. Soft Errors are radiation-induced effects while the radiation particles such as Alpha, Neutrons or Heavy Ions, interact…

Statistical inference on graphs is a burgeoning field in the applied and theoretical statistics communities, as well as throughout the wider world of science, engineering, business, etc. In many applications, we are faced with the reality…

Let $G$ be a graph and $A$ be its adjacency matrix. A graph $G$ is invertible if its adjacency matrix $A$ is invertible and the inverse of $G$ is a weighted graph with adjacency matrix $A^{-1}$. A signed graph $(G,\sigma)$ is a weighted…