Related papers: Structural and Spectral properties of Corona Graph…
The notion of corona of two graphs was introduced by Frucht and Harary in 1970. In this paper we generalize their definition of corona product of two graphs and introduce corona product of two signed graphs by utilizing the framework of…
Many graph products have been applied to generate complex networks with striking properties observed in real-world systems. In this paper, we propose a simple generative model for simplicial networks by iteratively using edge corona…
Two types of corona products for simple directed graphs are introduced, extending the classical notions from the undirected setting: the vertex-corona and the arc-corona. Their structural and spectral properties are investigated through the…
In this paper, we extend our earlier proposal of corona product of signed graphs into generalized corona product of signed graphs inspired by the generalized corona product of unsigned graphs. Then we study structural balance and spectral…
This paper introduces the concept of $\mu$-signed and duplication signed graphs and shows that both are always structurally balanced. Using the duplication signed graph, we define the corona product of the duplication signed graph…
In this paper, we introduce a generalization of corona of graphs. This construction generalizes the generalized corona of graphs (consequently, the corona of graphs), the cluster of graphs, the corona-vertex subdivision graph of graphs and…
We introduce recursive corona graphs as a model of small-world networks. We investigate analytically the critical characteristics of the model, including order and size, degree distribution, average path length, clustering coefficient, and…
Recently, real world networks having constant/shrinking diameter along with power-law degree distribution are observed and investigated in literature. Taking an inspiration from these findings, we propose a deterministic complex network…
Let $G_1$ and $G_2$ be two simple connected graphs. The invariant \textit{coronal} of graph is used in order to determine the $\alpha$-eigenvalues of four different types of graph equations that are $G_1 \circ G_2, G_1\lozenge G_1$ and the…
Various graph products and operations have been widely used to construct complex networks with common properties of real-life systems. However, current works mainly focus on designing models of binary networks, in spite of the fact that…
The paper focuses on studying strong geodetic sets and numbers in the context of corona-type products of graphs. Our primary focus is on three variations of the corona products: the generalized corona, generalized edge corona, and…
The corona of hypergraphs is an extension of the corona operation applied to graphs. The corona $G_0^* \odot_1^n G_1^*$ of two hypergraphs is obtained by taking $n$ copies of $G_1^*$ (where $n$ is the order of $G_0^*$) and by joining the…
In this paper, we study rooted products of graphs from the perspective of combinatorial commutative algebra. For edge ideals, we introduce the 2-Cohen-Macaulayness with respect to a vertex and use it to investigate when edge ideals of…
In this paper, we determine the two normalized Laplacian spectrum of generalized subdivision- vertex corona, subdivision-edge corona for a connected regular graph with an arbitrary reg- ular graph in terms of their normalized Laplacian…
For unsigned graphs G and H, the characteristic polynomial of different graph matrices for edge corona, subdivision vertex neighbourhood corona and subdivision edge neighbourhood corona has already been studied using the concept of coronal.…
Graph operations are crucial for building complicated network architectures from simple graphs. In [7], authors defined two new variants of Corona product and investigated some topological indices. In this paper, we extended the work and…
Determining and analyzing the spectra of graphs is an important and exciting research topic in theoretical computer science. The eigenvalues of the normalized Laplacian of a graph provide information on its structural properties and also on…
We introduce a new invariant, the coronal of a graph, and use it to compute the spectrum of the corona $G\circ H$ of two graphs $G$ and $H$. In particular, we show that this spectrum is completely determined by the spectra of $G$ and $H$…
We present the spectrum of the (normalized) graph Laplacian as a systematic tool for the investigation of networks, and we describe basic properties of eigenvalues and eigenfunctions. Processes of graph formation like motif joining or…
Spectral hypergraph theory has recently attracted considerable interest as it provides a natural framework for modeling higher-order relationships beyond classical graphs. In this setting, eigenvalues of adjacency, Laplacian, and…