Results 11 to 20 of about 11,443 (267)
Discrete Mathematics, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kinkar Ch Das, Seyed Ahmad Mojallal
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On net-Laplacian energy of signed graphs
Communications in Combinatorics and Optimization, 2017 A signed graph is a graph where the edges are assigned either positive or negative signs. Net degree of a signed graph is the difference between the number of positive and negative edges incident with a vertex. It is said to be net-regular if all its
Nutan G. Nayak
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On Laplacian-energy-like invariant and incidence energy [PDF]
International Journal of Group Theory, 2015 For a simple connected graph G with n -vertices having Laplacian eigenvalues μ 1 , μ 2 , … , μ n−1 , μ n =0 , and signless Laplacian eigenvalues q 1 ,q 2 ,…,q n , the Laplacian-energy-like invariant(LEL ) and the incidence energy ...
Shariefuddin Pirzada , Hilal A. Ganie
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, 2013 Summary: Let \(G\) be a connected graph of order \(n\) with Laplacian eigenvalues \(\mu_1\geq\mu_2\geq\cdots\geq\mu_{n-1}>\mu_n=0\). The Laplacian energy of the graph \(G\) is defined as \(LE=LE(G)=\sum_{i=1}^n| \mu_i-2m/n| \). Upper bounds for \(LE\) are obtained in terms of \(n\) and the number of edges \(m\).
Das, Kinkar Ch. +3 more
core +6 more sources
Linear Algebra and its Applications, 2006 The authors introduce the concept of Laplacian energy of a graph \(G\) by letting \(LE(G)=\sum_{i=1}^n | \mu_i - \frac{2m}{n}| \), where \(\mu_i\), \(i=1,\dots,n\), are the eigenvalues of the Laplacian matrix of \(G\). They show that the above definition is well chosen and much in analogy with the usual graph energy \(E(G)\), which is the sum of ...
Gutman, Ivan, Zhou, Bo
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Laplacian energy of union and Cartesian product and Laplacian equienergetic graphs [PDF]
Kragujevac Journal of Mathematics, 2015 The Laplacian energy of a graph G with n vertices and m edges is defined as LE(G) = ∑ni=1 |μi-2m/n|, where μ1, μ2,...,μn are the Laplacian eigenvalues of G. If two graphs G1 and G2 have equal average vertex degrees, then LE(G1 ∪ G2) = LE(G1) + LE(G2). Otherwise, this identity is violated. We determine a term Ξ, such that LE(G1) + LE(G2) - Ξ ≤LE(G1 ∪ G2)
Ramane H., Gudodagi G., Gutman, Ivan
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On the Laplacian-energy-like invariant
Linear Algebra and its Applications, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Das, Kinkar Ch. +2 more
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Laplacian energy of diameter 3 trees
Applied Mathematics Letters, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Vilmar Trevisan, Cybele T M Vinagre
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Laplacian energy of trees with at most 10 vertices
Indonesian Journal of Combinatorics, 2018 Let Tn be the set of all trees with n ≤ 10 vertices. We show that the Laplacian energy of any tree Tn is strictly between the Laplacian energy of the path Pn and the star Sn, partially proving the conjecture that this hold for any tree.
Masood Ur Rehman +2 more
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On the bounds for signless Laplacian energy of a graph
Discrete Applied Mathematics, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hilal A Ganie, S Pirzada
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