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Applicable analysis and discrete mathematics, ISSN 1452-8630, 4/2017, Volume 11, Issue 1, pp. 123 - 135
Let 𝐺 be a graph on 𝑛 vertices and its complement. In this paper, we prove a Nordhaus-Gaddum type inequality to the second largest eigenvalue of a graph 𝐺, λ₂(𝐺), when 𝐺... 
Line graphs | Integers | Maximum value | Linear algebra | Eigenvalues | Discrete mathematics | Mathematical inequalities | Spectral graph theory | Vertices | MATHEMATICS | MATHEMATICS, APPLIED | adjacency matrix | Nordhaus-Gaddum inequalities | BOUNDS | second largest eigenvalue of a graph
Journal Article
Applied mathematics and computation, ISSN 0096-3003, 01/2016, Volume 273, pp. 880 - 884
...–Gaddum-type inequality for the Wiener polarity index of a graph G of order n. Due to concerns that both Wp(G) and Wp(G... 
Complement | The Wiener polarity index | Nordhaus–Gaddum-type inequality | Extremal graph | Diameter | Nordhaus-Gaddum-type inequality | MATHEMATICS, APPLIED | NUMBER | TREES | CONGRUENCE RELATION | Nordhaus-Gaddum-type inequaliiy | VERSION | VERTICES | GRAPHS | Equality
Journal Article
Linear algebra and its applications, ISSN 0024-3795, 2019, Volume 564, pp. 236 - 263
We propose a Nordhaus–Gaddum conjecture for q(G), the minimum number of distinct eigenvalues of a symmetric matrix corresponding to a graph G: for every graph... 
Orthogonal matrices | Inverse eigenvalue problem for graphs | Minimum number of distinct eigenvalues | Minimum rank | Nordhaus–Gaddum inequality | MATHEMATICS | MATHEMATICS, APPLIED | Nordhaus-Gaddum inequality | RANK | Trees | Eigenvalues | Graphs | Mathematical analysis | Matrix methods | Eigen values
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 08/2019, Volume 267, pp. 176 - 183
...–Gaddum type inequalities for μ1(G) and μ2(G). We improve some existing results from the literature for μ1(G... 
Laplacian eigenvalues | Laplacian matrix | Nordhaus–Gaddum inequality | MATHEMATICS, APPLIED | TREES | SPREAD | Nordhaus-Gaddum inequality | Eigenvalues | Graph theory | Apexes | Inequalities | Eigen values
Journal Article
Applied mathematics and computation, ISSN 0096-3003, 2020, Volume 365, p. 124716
For a real number alpha is an element of [0, 1], the A(alpha)-matrix of a graph G is defined as A(alpha)(G) = alpha D(G) + (1 - alpha)A(G), where A(G) and D(G)... 
EIGENVALUE | A(alpha)-matrix | MATHEMATICS, APPLIED | Spectral radius | Nordhaus-Gaddum | A(ALPHA)-SPECTRAL RADIUS | ALPHA-INDEX | SPECTRAL-RADIUS | GRAPHS
Journal Article
Applied mathematics and computation, ISSN 0096-3003, 01/2020, Volume 365
For a real number α ∈ [0, 1], the Aα-matrix of a graph G is defined as Aα(G)=αD(G)+(1−α)A(G), where A(G) and D(G) are the adjacency matrix and diagonal degree... 
Aα-matrix | Nordhaus–Gaddum | Spectral radius
Journal Article
by Chen, YY and Li, D and Meng, JX
Linear algebra and its applications, ISSN 0024-3795, 10/2020, Volume 602, pp. 57 - 72
Let G be a graph with adjacency matrix A(G) and the degree diagonal matrix D(G). For any real alpha is an element of [0, 1], the matrix A(alpha) (G) of a graph... 
MATHEMATICS | MATHEMATICS, APPLIED | Quotient matrix | EIGENVALUE PROBLEMS | The second largest A(alpha)-eigenvalue | A(ALPHA)-SPECTRAL RADIUS | Nordhaus-Gaddum type inequalities
Journal Article
Discrete mathematics, ISSN 0012-365X, 2019, Volume 342, Issue 5, pp. 1318 - 1324
...¯ is the complement of G and χ is the chromatic number. We study similar inequalities for χg(G) and colg(G), which denote, respectively, the game chromatic number and the game coloring number of G... 
Marking game | Coloring game | Nordhaus–Gaddum type inequalities | MATHEMATICS | Nordhaus-Gaddum type inequalities | GRAPHS | Mathematics
Journal Article
Bulletin of the Malaysian Mathematical Sciences Society, ISSN 2180-4206, 2018, Volume 42, Issue 5, pp. 2603 - 2621
... of $$D^{Q}(G)$$ D Q ( G ) . In this paper, we study Nordhaus–Gaddum-type inequalities for distance signless Laplacian eigenvalues of graphs and present some new upper... 
05C12 | Line graph | 05C50 | Spectral radius | Transmission regular | Nordhaus–Gaddum-type inequalities | Distance signless Laplacian matrix | Mathematics, general | Mathematics | Applications of Mathematics | 15A18 | MATHEMATICS | MATRIX | WIENER | ENERGY | RADIUS | Nordhaus-Gaddum-type inequalities | SHARP BOUNDS | Eigenvalues | Lower bounds | Graphs | Graph theory
Journal Article
SIAM journal on discrete mathematics, ISSN 1095-7146, 2009, Volume 23, Issue 3, pp. 1575 - 1586
... that R(G) 8n/11 when (G) 2 and n 9, and this is sharp. Key words. domination, Roman domination number, NordhausGaddum inequality AMS subject classications. 05C69... 
Domination | Roman domination number | Nordhaus-Gaddum inequality | GRAPH | MATHEMATICS, APPLIED | domination | EMPIRE | Lower bounds | Graphs | Labels | Roman | Marking | Mathematical analysis
Journal Article
Linear algebra and its applications, ISSN 0024-3795, 10/2020, Volume 602, pp. 57 - 72
Let G be a graph with adjacency matrix A(G) and the degree diagonal matrix D(G). For any real α∈[0,1], the matrix Aα(G) of a graph is defined as... 
Quotient matrix | The second largest [formula omitted]-eigenvalue | Nordhaus-Gaddum type inequalities
Journal Article
Discrete mathematics, algorithms, and applications, ISSN 1793-8309, 04/2017, Volume 9, Issue 2
Journal Article
Theoretical computer science, ISSN 0304-3975, 02/2013, Volume 471, pp. 74 - 83
.... In this paper, we investigate the Nordhaus–Gaddum-type inequality of a 3-decomposition of Kn for the hyper-Wiener index: 7n2≤WW(G1)+WW(G2)+WW(G3)≤2n+24+n2+4(n−1... 
Wiener index | Hyper-Wiener index | [formula omitted]-decomposition | Nordhaus–Gaddum-type inequality | k-decomposition | Nordhaus-Gaddum-type inequality | Nordhaus Gaddum-type inequality | COMPUTER SCIENCE, THEORY & METHODS | TREES | Equality
Journal Article
Applied mathematics letters, ISSN 0893-9659, 11/2012, Volume 25, Issue 11, pp. 1701 - 1707
.... In this contribution, we investigate the Nordhaus–Gaddum-type inequality of a k-decomposition of Kn for the general Zagreb index and a 2-decomposition for the Zagreb co-indices, respectively... 
The Zagreb co-index | Nordhaus–Gaddum-type inequality | The general Zagreb index | Nordhaus-Gaddum-type inequality | MATHEMATICS, APPLIED | 1ST | CONNECTIVITY INDEX
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 1/2012, Volume 28, Issue 1, pp. 123 - 131
A set S of vertices in a graph G is a connected dominating set if every vertex not in S is adjacent to some vertex in S and the subgraph induced by S is... 
Nordhaus–Gaddum inequalities | Connected dominating set | Connected domination number | Mathematics | Engineering Design | Combinatorics | 05C69 | Nordhaus-Gaddum inequalities | MATHEMATICS | SPANNING-TREES | MINIMUM DEGREE | LEAVES | Universities and colleges | Graphs | Complement | Combinatorial analysis
Journal Article
Contributions to discrete mathematics, ISSN 1715-0868, 2020, Volume 15, Issue 1, pp. 154 - 162
We study the Nordhaus-Gaddum type results for (k-1, k, j) and k-domination numbers of a graph G and investigate these bounds for the k-limited packing and... 
MATHEMATICS | total domination number | Nordhaus-Gaddum inequality | packing number | k-domination number | open packing number
Journal Article
Transactions on combinatorics, ISSN 2251-8657, 03/2018, Volume 7, Issue 1, pp. 31 - 36
... for $lambda_{1}$ and Aouchiche and Hansen's conjecture for $q_1$ in Nordhaus-Gaddum type inequalities‎. ‎Furthermore‎, ‎by the properties of the products of graphs we put forward a new approach to find some bounds of Nordhaus-Gaddum type... 
extremal graphs | Nordhaus-Gaddum inequalities | product of graphs
Journal Article
Linear algebra and its applications, ISSN 0024-3795, 2019, Volume 581, pp. 336 - 353
Let G be a graph of order n, and let q1(G)≥q2(G)≥⋯≥qn(G) denote the signless Laplacian eigenvalues of G. Ashraf and Tayfeh-Rezaie (2014) [3] showed that... 
Signless Laplacian eigenvalue | Quotient matrix | Nordhaus–Gaddum type inequalities | Interlacing | MATHEMATICS | MATHEMATICS, APPLIED | SPREAD | Nordhaus-Gaddum type inequalities | 2ND LARGEST EIGENVALUE | Eigenvalues | Graphs
Journal Article
ELECTRONIC JOURNAL OF COMBINATORICS, ISSN 1077-8926, 07/2014, Volume 21, Issue 3
Let G be a graph with n vertices. We denote the largest signless Laplacian eigenvalue of G by q(1)(G) and Laplacian eigenvalues of G by mu(1)(G) >= ... >=... 
MATHEMATICS | MATHEMATICS, APPLIED | Laplacian spread | Signless Laplacian eigenvalues of graphs | Laplacian eigenvalues of graphs | SPREAD | Nordhaus-Gaddum type inequalities
Journal Article
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