Related papers: Spectra of generalized corona of graphs constraine…
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…
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…
In this paper, we introduce central vertex corona, central edge corona, and central edge neighborhood corona of graphs using central graph. Also, we determine their adjacency spectrum, Laplacian spectrum and signless Laplacian spectrum.…
The $T$-graph $T(G)$ of a graph $G$ is the graph whose vertices are the vertices and edges of $G$, with two vertices of $T(G)$ are adjacent if and only if the corresponding elements of $G$ are adjacent or incident. In this paper, we…
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.…
Let $G=(V(G),E(G))$ be a graph with vertex set $V(G)$ and edge set $E(G)$. The subdivision graph $\mathcal{S}(G)$ of a graph $G$ is the graph obtained by inserting a new vertex into every edge of $G$. Let $G_1$ and $G_2$ be two vertex…
Let $G, H_{i}$ be simple graphs with $n=|V(G)|$, $m=|E(G)|$ and $i=1, 2, \ldots, n(m)$. The generalized corona, denoted $G\tilde{o}\wedge^{n}_{i=1} H_{i}$, is the graph obtained by taking one copy of graphs $G, H_{1},\ldots, H_{n}$ and…
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…
Typically, graph structures are represented by one of three different matrices: the adjacency matrix, the unnormalised and the normalised graph Laplacian matrices. The spectral (eigenvalue) properties of these different matrices are…
Given simple graphs $G_1$ and $G_2$, the neighbourhood corona of $G_1$ and $G_2$, denoted $G_1\star G_2$, is the graph obtained by taking one copy of $G_1$ and $|V(G_1)|$ copies of $G_2$, and joining the neighbours of the $i$th vertex of…
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…
For a simple graph $G$, the generalized adjacency matrix $A_{\alpha}(G)$ is defined as $A_{\alpha}(G)=\alpha D(G)+(1-\alpha)A(G), \alpha\in [0,1]$, where $A(G)$ is the adjacency matrix and $D(G)$ is the diagonal matrix of vertex degrees of…
Product graphs have been gainfully used in literature to generate mathematical models of complex networks which inherit properties of real networks. Realizing the duplication phenomena imbibed in the definition of corona product of two…
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 $H$…
The subdivision graph $\mathcal{S}(G)$ of a graph $G$ is the graph obtained by inserting a new vertex into every edge of $G$. Let $G_1$ and $G_2$ be two vertex disjoint graphs. The \emph{subdivision-vertex corona} of $G_1$ and $G_2$,…
In this paper, for a graph G and a family of partitions P of vertex neighborhoods of G, we define the general corona G \circ P of G. Among several properties of this new operation, we focus on application general coronas to a new kind of…
A signed graph $S=(G, \sigma)$ is a pair in which $G$ is an underlying graph and $\sigma$ is a function from the edge set to $\{\pm1\}$. For signed graphs $S_{1}$ and $S_{2}$ on $n_{1}$ and $n_{2}$ vertices, respectively, the signed…
For simple graphs $G$, $G_1$ and $G_2$, we denote their double corona based on $R$-graph by $G^{(R)}\otimes{\{G_1,G_2\}}$. This paper determines the normalized Laplacian spectrum of $G^{(R)}\otimes{\{G_1,G_2\}}$ in terms of these of $G$,…
In this paper, we introduce two new graph operations, namely, the subdivision vertex-edge neighbourhood vertex-corona and the subdivision vertex-edge neighbourhood edge-corona on graphs $G_1$, $G_2$ and $G_3$, and the resulting graphs are…
Graphs can be associated with a matrix according to some rule and we can find the spectrum of a graph with respect to that matrix. Two graphs are cospectral if they have the same spectrum. Constructions of cospectral graphs help us…