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Laplacian energy of a graph
Let G be a graph with n vertices and m edges. Let λ1, λ2, … , λn be the eigenvalues of the adjacency matrix of G, and let μ1, μ2, … , μn be the eigenvalues of the Laplacian matrix of G. An earlierExpand
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On a novel connectivity index
We present a novel connectivity index for (molecular) graphs, called sum-connectivity index and give several basic properties for this index, especially lower and upper bounds in terms of graphExpand
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On general sum-connectivity index
We report some properties especially lower and upper bounds in terms of other graph invariants for the general sum-connectivity index which generalizes both the ordinary sum-connectivity index andExpand
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A connection between ordinary and Laplacian spectra of bipartite graphs
Let G be a bipartite graph with n vertices and m edges. Let S(G) be the subdivision of G, obtained by inserting a new vertex on each edge of G. The ordinary characteristic polynomial of S(G) and theExpand
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On sum of powers of the Laplacian eigenvalues of graphs
Abstract For a graph G and a real α ≠ 0 , we study the graph invariant s α ( G ) – the sum of the α th power of the non-zero Laplacian eigenvalues of G . The cases α = 2 , 1 2 and - 1 have appearedExpand
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On Atom-Bond Connectivity Index
The atom-bond connectivity (ABC) index, introduced by Estrada et al. in 1998, displays an excellent correlation with the formation heat of alkanes. We give upper bounds for this graph invariant usingExpand
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On the revised Szeged index
We give bounds for the revised Szeged index, and determine the n-vertex unicyclic graphs with the smallest, the second-smallest and the third-smallest revised Szeged indices for n>=5, and theExpand
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On reformulated Zagreb indices
  • A. Ilic, B. Zhou
  • Mathematics, Computer Science
  • Discret. Appl. Math.
  • 1 February 2012
The first and second reformulated Zagreb indices are defined respectively in terms of edge-degrees as EM"1(G)=@?"e"@?"Edeg(e)^2 and EM"2(G)=@?"e"~"fdeg(e)deg(f), where deg(e) denotes the degree ofExpand
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ON ECCENTRIC CONNECTIVITY INDEX
The eccentric connectivity index, proposed by Sharma, Goswami and Madan, has been employed successfully for the development of numerous mathematical models for the prediction of biological activitiesExpand
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Spectra of graph operations based on R-graph
For a regular graph and an arbitrary graph , we determine the adjacency (respectively, Laplacian and signless Laplacian) spectra of four types of graph operations on and involving the R-graph of ,Expand
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