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Unicyclic graphs with equal Laplacian energy [PDF]
Linear and Multilinear Algebra, 2013 11 pages, 11 figures, slightly modified version of Theorem 1 when compared with original ...
Eliseu Fritscher +2 more
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On Laplacian resolvent energy of graphs [PDF]
Transactions on Combinatorics, 2023 Let $G$ be a simple connected graph of order $n$ and size $m$. The matrix $L(G)=D(G)-A(G)$ is the Laplacian matrix of $G$, where $D(G)$ and $A(G)$ are the degree diagonal matrix and the adjacency matrix, respectively. For the graph $G$, let $d_{1}\geq d_{
Sandeep Bhatnagar +2 more
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Vertex weighted Laplacian Energy of union of graphs [PDF]
Computer Science Journal of Moldova, 2018 The vertex weighted Laplacian energy with respect to the vertex weight $w$ of a graph $G$ with $n$ vertices is defined as ~$LE_w(G)=\sum\limits_{i=1}^n|\mu_i-\bar{w}|$, where ${{\mu }_{1}},{{\mu }_{2}},...,{{\mu }_{n}}$ are the Laplacian eigenvalues of ...
Nilanjan De
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On a conjecture of Laplacian energy of trees [PDF]
Discrete Mathematics, Algorithms and Applications, 2021 Let [Formula: see text] be a simple graph with [Formula: see text] vertices, [Formula: see text] edges having Laplacian eigenvalues [Formula: see text]. The Laplacian energy LE[Formula: see text] is defined as LE[Formula: see text], where [Formula: see text] is the average degree of [Formula: see text]. Radenković and Gutman conjectured that among all
Hilal A. Ganie +2 more
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On distance Laplacian energy in terms of graph invariants [PDF]
, 2023 summary:For a simple connected graph $G$ of order $n$ having distance Laplacian eigenvalues $ \rho ^{L}_{1}\geq \rho ^{L}_{2}\geq \cdots \geq \rho ^{L}_{n}$, the distance Laplacian energy ${\rm DLE} (G)$ is defined as ${\rm DLE} (G)=\sum _{i=1}^{n}|\rho ^
Rather, Bilal A. +3 more
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Novel Concept of Energy in Bipolar Single-Valued Neutrosophic Graphs with Applications
Axioms, 2021 The energy of a graph is defined as the sum of the absolute values of its eigenvalues. Recently, there has been a lot of interest in graph energy research.
Siti Nurul Fitriah Mohamad +3 more
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Local Energy Estimates for the Fractional Laplacian [PDF]
SIAM Journal on Numerical Analysis, 2021 The integral fractional Laplacian of order $s \in (0,1)$ is a nonlocal operator. It is known that solutions to the Dirichlet problem involving such an operator exhibit an algebraic boundary singularity regardless of the domain regularity. This, in turn, deteriorates the global regularity of solutions and as a result the global convergence rate of the ...
Juan Pablo Borthagaray +2 more
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Signless Laplacian energy, distance Laplacian energy and distance signless Laplacian spectrum of unitary addition Cayley graphs [PDF]
Linear and Multilinear Algebra, 2021 In this paper we compute bounds for signless Laplacian energy, distance signless Laplacian eigenvalues and signless Laplacian energy of unitary addition Cayley graph G_{n}. We also obtain distance Laplacian eigenvalues and distance Laplacian energy of G_{n}.
P., Naveen, A. V, Chithra
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Bounds on Energy and Laplacian Energy of Graphs [PDF]
Journal of the Indonesian Mathematical Society, 2017 Let G be simple graph with n vertices and m edges. The energy E(G) of G, denotedby E(G), is dened to be the sum of the absolute values of the eigenvalues of G. Inthis paper, we present two new upper bounds for energy of a graph, one in terms ofm,n and another in terms of largest absolute eigenvalue and the smallest absoluteeigenvalue.
Sridhara, G., Kanna, Rajesh M. R.
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