Related papers: A Novel Method to Construct NSSD Molecular Graphs
In the analysis of large-scale network data, a fundamental operation is the comparison of observed phenomena to the predictions provided by null models: when we find an interesting structure in a family of real networks, it is important to…
An eigenvalue of a graph $G$ is called a main eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. It is well known that a graph $G$ has exactly two main eigenvalues if and only if there exists a unique pair of…
Signed graphs, which are characterized by both positive and negative edge weights, have recently attracted significant attention in the field of graph signal processing (GSP). Existing works on signed graph learning typically assume that…
The graph reconstruction conjecture states that all graphs on at least three vertices are determined up to isomorphism by their deck. In this paper, a general framework for this problem is proposed to simply explain the reconstruction of…
A dominating set $S$ is an Isolate Dominating Set (IDS) if the induced subgraph $G[S]$ has at least one isolated vertex. In this paper, we initiate the study of new domination parameter called, isolate secure domination. An isolate…
Let $G$ be a finite group and $N$ a normal subgroup of $G$. We determine the structure of $N$ when the graph $\Gamma_G(N)$, which is the graph associated to the conjugacy classes of $G$ contained in $N$, has no triangles and when the graph…
Low density graphs are considered to be a realistic graph class for modelling road networks. It has advantages over other popular graph classes for road networks, such as planar graphs, bounded highway dimension graphs, and spanners. We…
Directed graphs are widely used to model asymmetric relationships in real-world systems. However, existing directed graph neural networks often struggle to jointly capture directional semantics and global structural patterns due to their…
Graph Neural Networks (GNNs) have emerged as a promising tool to handle data exhibiting an irregular structure. However, most GNN architectures perform well on homophilic datasets, where the labels of neighboring nodes are likely to be the…
The ideal (tagged resp.) triangulation of bounded surface with marked points are associated with skew-symmetric (skew-symmetrizable) exchange matrices. An algo- rithm is established to decompose the graph associated to such matrix. There…
An eigenvalue of the adjacency matrix of a graph is said to be \emph{main} if the all-1 vector is not orthogonal to the associated eigenspace. In this work, we approach the main eigenvalues of some graphs. The graphs with exactly two main…
Construction of non-isomorphic cospectral graphs is a nontrivial problem in spectral graph theory specially for large graphs. In this paper, we establish that graph theoretical partial transpose of a graph is a potential tool to create…
Directed acyclic graphs (DAGs) are a class of graphs commonly used in practice, with examples that include electronic circuits, Bayesian networks, and neural architectures. While many effective encoders exist for DAGs, it remains…
We consider the problem of molecular graph generation using deep models. While graphs are discrete, most existing methods use continuous latent variables, resulting in inaccurate modeling of discrete graph structures. In this work, we…
A cograph is a simple graph which contains no path on 4 vertices as an induced subgraph. The vicinal preorder on the vertex set of a graph is defined in terms of inclusions among the neighborhoods of vertices. The minimum number of chains…
In this paper, our goal is to characterize two graph classes based on the properties of minimal vertex (edge) separators. We first present a structural characterization of graphs in which every minimal vertex separator is a stable set. We…
Graph drawing addresses the problem of finding a layout of a graph that satisfies given aesthetic and understandability objectives. The most important objective in graph drawing is minimization of the number of crossings in the drawing, as…
We introduce a dense counterpart of graph degeneracy, which extends the recently-proposed invariant symmetric difference. We say that a graph has sd-degeneracy (for symmetric-difference degeneracy) at most $d$ if it admits an elimination…
We consider the graphs whose edges are marked by the integers (weights) from $0$ to $q-1$ (zero corresponds to no-edge). Such graph is called additive if its vertices can be marked in such a way that the weight of every edge is equal to the…
Strongly chordal graphs are a subclass of chordal graphs. The interest in this subclass stems from the fact that many problems which are NP-complete for chordal graphs are solvable in polynomial time for this subclass. However, we are not…