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pro vyhledávání: '"Pirzada, S."'
In this article, we explore the concept of spectral redundancy within the class of pineapple graphs, denoted as $\mathcal{P}(\alpha,\beta)$. These graphs are constructed by attaching $\beta$ pendent edges to a single vertex of a complete graph $K_\al
Externí odkaz:
http://arxiv.org/abs/2405.05992
Autor:
Rehman, Amir, Pirzada, S.
Let $G$ be a simple connected graph of size $m$. Let $A$ be the adjacency matrix of $G$ and let $\rho(G)$ be the spectral radius of $G$. A graph is said to be $H$-free if it does not contain a subgraph isomorphic to $H$. Let $H(\ell,3)$ be the graph
Externí odkaz:
http://arxiv.org/abs/2401.03787
In this paper, we introduce a new graph structure, called the $direct~ sum ~graph$ on a finite dimensional vector space. We investigate the connectivity, diameter and the completeness of $\Gamma_{U\oplus W}(\mathbb{V})$. Further, we find its dominati
Externí odkaz:
http://arxiv.org/abs/2310.00251
Let $\Gamma=(G, \sigma)$ be a signed graph of order $n$ with eigenvalues $\mu_1,\mu_2,\ldots,\mu_n.$ We define the Estrada index of a signed graph $\Gamma$ as $EE(\Gamma)=\sum_{i=1}^ne^{\mu_i}$. We characterize the signed unicyclic graphs with the ma
Externí odkaz:
http://arxiv.org/abs/2309.13252
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 neighbourhood cor
Externí odkaz:
http://arxiv.org/abs/2305.02964
For a graph $G$, the generalized adjacency matrix $A_\alpha(G)$ is the convex combination of the diagonal matrix $D(G)$ and the adjacency matrix $A(G)$ and is defined as $A_\alpha(G)=\alpha D(G)+(1-\alpha) A(G)$ for $0\leq \alpha \leq 1$. This matrix
Externí odkaz:
http://arxiv.org/abs/2304.00554
Autor:
Singh, Karam Ratan1, Pirzada, S.2 pirzadasd@kashmiruniversity.ac.in
Publikováno v:
Kuwait Journal of Science. Oct2024, Vol. 51 Issue 4, p1-5. 5p.
Autor:
Khan, Saleem, Pirzada, S.
Let $G$ be a simple connected simple graph of order $n$. The distance Laplacian matrix $D^{L}(G)$ is defined as $D^L(G)=Diag(Tr)-D(G)$, where $Diag(Tr)$ is the diagonal matrix of vertex transmissions and $D(G)$ is the distance matrix of $G$. The eige
Externí odkaz:
http://arxiv.org/abs/2210.10579
Autor:
Pirzada, S., Khan, Saleem
The reciprocal distance Laplacian matrix of a connected graph $G$ is defined as $RD^L(G)=RT(G)-RD(G)$, where $RT(G)$ is the diagonal matrix of reciprocal distance degrees and $RD(G)$ is the Harary matrix. Since $RD^L(G)$ is a real symmetric matrix, w
Externí odkaz:
http://arxiv.org/abs/2208.13216
Let $\Gamma=(G,\sigma)$ be a signed graph, where $\sigma$ is the sign function on the edges of $G$. In this paper, we use the operation of partial transpose to obtain non-isomorphic Laplacian cospectral signed graphs. We will introduce two new operat
Externí odkaz:
http://arxiv.org/abs/2205.08705