Related papers: On Weakly Uniform Integer Additive Set-Indexers of…
In this short survey article, we present an elementary, yet quite powerful, method of enumerating independent sets in graphs. This method was first employed more than three decades ago by Kleitman and Winston and has subsequently been used…
We characterize the bipartite graphs that minimize the (first-degree based) entropy, among all bipartite graphs of given size, or given size and (upper bound on the) order. The extremal graphs turn out to be complete bipartite graphs, or…
Let $R$ be a $G$-graded ring. In this article, we introduce two new concepts on graded rings, namely, weakly graded rings and invertible graded rings, and we discuss the relations between these concepts and several properties of graded…
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…
A graph polynomial $P$ is weakly distinguishing if for almost all finite graphs $G$ there is a finite graph $H$ that is not isomorphic to $G$ with $P(G)=P(H)$. It is weakly distinguishing on a graph property $\mathcal{C}$ if for almost all…
In relational DBMS, window functions have been widely used to facilitate data analytics. Surprisingly, while similar concepts have been employed for graph analytics, there has been no explicit notions of graph window analytic functions. In…
In this paper we provide a principled approach to solve a transductive classification problem involving a similar graph (edges tend to connect nodes with same labels) and a dissimilar graph (edges tend to connect nodes with opposing…
This is a survey article featuring some of Wolmer Vasconcelos' contributions to commutative algebra, and explaining how Vasconcelos' work and insights have contributed to the development of commutative algebra and its interaction with other…
Inductive $k$-independent graphs generalize chordal graphs and have recently been advocated in the context of interference-avoiding wireless communication scheduling. The NP-hard problem of finding maximum-weight induced $c$-colorable…
We introduce Integrated Weak Learning, a principled framework that integrates weak supervision into the training process of machine learning models. Our approach jointly trains the end-model and a label model that aggregates multiple…
Nine variations of the concept of domination in a simple graph are identified as fundamental domination concepts, and a unified approach is introduced for studying them. For each variation, the minimum cardinality of a subset of dominating…
High-quality labels are often very scarce, whereas unlabeled data with inferred weak labels occurs more naturally. In many cases, these weak labels dictate the frequency of each respective class over a set of instances. In this paper, we…
Common quality metrics of graph drawing have been about the readability criteria, such as small number of edge crossings, small drawing area and small total edge length. Bold graph drawing considers more realistic drawings consisting of…
The concept of geometric-arithmetic index was introduced in the chemical graph theory recently, but it has shown to be useful. The aim of this paper is to obtain new inequalities involving the geometric-arithmetic index $GA_1$ and…
In this paper, we define a class of auxiliary graphs associated with simple undirected graphs. This class of auxiliary graphs is based on the set of spanning trees of the original graph and the edges constituting those spanning trees. A…
This paper proposes a Mixed-Integer Linear Programming approach for the Soft Graph Clustering Problem. This is the first method that simultaneously allocates membership proportion for vertices that lie in multiple clusters, and that…
The study of essential and strongly essential variables in functions defined on finite sets is a part of $k$-valued logic. We extend the main definitions from functions to terms. This allows us to apply concepts and results of Universal…
We introduce a type of graph integrals which are holomorphic analogs of configuration space integrals. We prove their (ultraviolet) finiteness by considering a compactification of the moduli space of graphs with metrics, and study their…
Various algorithms have been proposed to enumerate all connected induced subgraphs of a graph $G=(V,E)$. As a variation we enumerate all "packings of connected sets", i.e. partitions $\Pi$ of $V$ with the property that each part of $\Pi$…
In this paper, we exhibit the equivalence between different notions of unique range sets, namely, unique range sets, weighted unique range sets and weak-weighted unique range sets under certain conditions.\par Also, we present some…