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Theoretical computer science, ISSN 0304-3975, 2019, Volume 759, pp. 61 - 71
The matching preclusion number of a graph G, denoted by mp(G), is the minimum number of edges whose deletion results in a graph that has neither perfect... 
Nordhaus–Gaddum problem | Perfect matching | Extremal problem | Matching preclusion number | Interconnection networks | COMPUTER SCIENCE, THEORY & METHODS | Nordhaus-Gaddum problem
Journal Article
AKCE International Journal of Graphs and Combinatorics, ISSN 0972-8600, 2018, Volume 17, Issue 1, pp. 86 - 97
Imagine that we are given a set D of officials and a set W of civils. For each civil x∈W, there must be an official v∈D that can serve  x, and whenever any... 
Domination | Nordhaus–Gaddum | Corona | Certified domination | certified domination | nordhaus–gaddum | domination | corona
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
Bulletin of the Malaysian Mathematical Sciences Society, ISSN 2180-4206, 2018, Volume 42, Issue 5, pp. 2603 - 2621
Let G be a simple, connected graph, D(G) be the distance matrix of G, and Tr(G) be the diagonal matrix of vertex transmissions of G. The distance signless... 
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
Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 9/2019, Volume 42, Issue 5, pp. 1907 - 1920
Let D be a finite and simple digraph with vertex set V(D). A double Roman dominating function (DRDF) on a digraph D is a function $$f:V(D)\rightarrow... 
05C20 | Nordhaus–Gaddum | Signed domination | Double Roman domination | Mathematics, general | Roman domination | Mathematics | Applications of Mathematics | Digraph | 05C69 | k -domination | k-domination | MATHEMATICS | NUMBERS | Nordhaus-Gaddum | Minimum weight | Mathematical functions | Graph theory
Journal Article
Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 7/2018, Volume 41, Issue 3, pp. 1199 - 1209
A path P in an edge-colored graph G is called a proper path if no two adjacent edges of P are colored the same, and G is proper connected if every two vertices... 
Proper path | 05C50 | Complement graph | 05C40 | Mathematics | 15A18 | 92E10 | Mathematics, general | Applications of Mathematics | Nordhaus–Gaddum-type | Proper connection number | 05C35 | Diameter | 05C38 | MATHEMATICS | Nordhaus-Gaddum-type | RAINBOW CONNECTION | Graphs | Graph theory | Graph coloring | Upper bounds
Journal Article
Discrete mathematics, ISSN 0012-365X, 07/2015, Volume 338, Issue 7, pp. 1252 - 1263
For any real number α, let sα(G) denote the sum of the αth power of the non-zero Laplacian eigenvalues of a graph G. In this paper, we first obtain sharp... 
Laplacian-energy-like invariant | Kirchhoff index | Nordhaus–Gaddum-type | Laplacian eigenvalues | Matching number | Nordhaus-Gaddum-type | MATHEMATICS | ENERGY-LIKE INVARIANT | CONNECTIVITY
Journal Article
Journal of combinatorial optimization, ISSN 1573-2886, 2017, Volume 35, Issue 1, pp. 126 - 133
Journal Article
Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 1/2019, Volume 42, Issue 1, pp. 381 - 390
A graph is said to be total-colored if all the edges and the vertices of the graph are colored. A path P in a total-colored graph G is called a total-proper... 
Total-proper connection number | Total-proper path | 05C40 | Mathematics, general | Mathematics | Applications of Mathematics | Nordhaus–Gaddum-type | Complementary graph | 05C35 | 05C38 | 05C15 | MATHEMATICS | Nordhaus-Gaddum-type
Journal Article
Discrete mathematics, ISSN 0012-365X, 2008, Volume 308, Issue 7, pp. 1080 - 1087
Let G = ( V , E ) be a graph. A set S ⊆ V is a total restrained dominating set if every vertex is adjacent to a vertex in S and every vertex of V - S is... 
Domination | Nordhaus–Gaddum | Restrained | Total | Nordhaus-Gaddum | MATHEMATICS | restrained | total | domination
Journal Article
SIAM journal on discrete mathematics, ISSN 1095-7146, 2009, Volume 23, Issue 3, pp. 1575 - 1586
A Roman dominating function of a graph G is a labeling f : V(G) --> {0, 1, 2} such that every vertex with label 0 has a neighbor with label 2. The Roman... 
Domination | Roman domination number | Nordhaus-Gaddum inequality | GRAPH | MATHEMATICS, APPLIED | domination | EMPIRE | Lower bounds | Graphs | Labels | Roman | Marking | Mathematical analysis
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 08/2016, Volume 36, Issue 3, pp. 695 - 707
Two decades ago, resistance distance was introduced to characterize “chemical distance” in (molecular) graphs. In this paper, we consider three resistance... 
multiplicative degree-Kirchhoff index | additive degree-Kirchhoff index | resistance distance | Kirchhoff index | Nordhaus-Gaddum-type result | Nordhaus-gaddum-type re- sult | Resistance distance | Additive degree-kirchhoff index | Multiplicative degree-kirchhoff index | MATHEMATICS | CYCLICITY | WIENER | LAPLACIAN SPECTRUM
Journal Article
Results in Mathematics, ISSN 1422-6383, 9/2016, Volume 70, Issue 1, pp. 173 - 182
A vertex-colored graph G is rainbow vertex connected if any two distinct vertices are connected by a path whose internal vertices have distinct colors. The... 
total rainbow path | rainbow vertex connected | 05C40 | Mathematics | Vertex-coloring | total rainbow connected | triangle-free | total-coloring | complementary graph | Mathematics, general | Nordhaus–Gaddum-type | vertex rainbow path | 05C15 | Nordhaus-Gaddum-type | MATHEMATICS, APPLIED | MATHEMATICS | VERTEX-CONNECTION | COMPLEXITY
Journal Article
Journal of Combinatorial Optimization, ISSN 1382-6905, 5/2017, Volume 33, Issue 4, pp. 1443 - 1453
Journal Article
Discrete mathematics, algorithms, and applications, ISSN 1793-8309, 04/2017, Volume 9, Issue 2
Journal Article
Applied mathematics and computation, ISSN 0096-3003, 2018, Volume 338, pp. 669 - 675
A double Roman dominating function of a graph G is a labeling f: V(G) → {0, 1, 2, 3} such that if f(v)=0, then the vertex v must have at least two neighbors... 
Double Roman domination | Nordhaus–Gaddum type problem | Algorithm | Cograph | Double Roman domination number | MATHEMATICS, APPLIED | Nordhaus-Gaddum type problem
Journal Article
Discrete mathematics, ISSN 0012-365X, 2009, Volume 309, Issue 13, pp. 4522 - 4526
In this paper we will prove that μ ( G ) + μ ( G ¯ ) ≤ 1 + 3 2 n − 1 . where μ ( G ) , μ ( G ¯ ) are the greatest eigenvalues of the adjacency matrices of the... 
Eigenvalue | Nordhaus–Gaddum type problem | Spectral radius | Nordhaus-Gaddum type problem | MATHEMATICS | EDGES | NETWORK RELIABILITY | 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
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 02/2019, Volume 39, Issue 1, pp. 13 - 21
A vertex subset S of a digraph D is called a dominating set of D if every vertex not in S is adjacent from at least one vertex in S. The domination number of a... 
05C20 | domination number | Roman domination number | 05C69 | digraph | Nordhaus-Gaddum | Digraph | Domination number | MATHEMATICS | NUMBERS | STRONG EQUALITY
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 2019, Volume 255, pp. 167 - 182
An edge-colored graph G is conflict-free connected if, between each pair of distinct vertices of G, there exists a path in G containing a color used on exactly... 
Edge-coloring | Conflict-free connection number | Connectivity | Nordhaus–Gaddum-type result | MATHEMATICS, APPLIED | FREE COLORINGS | THEOREM | UNIQUE-MAXIMUM | REGIONS | Nordhaus-Gaddum-type result | NORDHAUS-GADDUM INEQUALITIES | Lower bounds | Graphs | Trees (mathematics) | Graph theory | Graph coloring | Apexes
Journal Article
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