Theoretical computer science, ISSN 03043975, 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  NordhausGaddum problem
Nordhaus–Gaddum problem  Perfect matching  Extremal problem  Matching preclusion number  Interconnection networks  COMPUTER SCIENCE, THEORY & METHODS  NordhausGaddum problem
Journal Article
AKCE International Journal of Graphs and Combinatorics, ISSN 09728600, 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
Domination  Nordhaus–Gaddum  Corona  Certified domination  certified domination  nordhaus–gaddum  domination  corona
Journal Article
Linear algebra and its applications, ISSN 00243795, 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  NordhausGaddum inequality  RANK  Trees  Eigenvalues  Graphs  Mathematical analysis  Matrix methods  Eigen values
Orthogonal matrices  Inverse eigenvalue problem for graphs  Minimum number of distinct eigenvalues  Minimum rank  Nordhaus–Gaddum inequality  MATHEMATICS  MATHEMATICS, APPLIED  NordhausGaddum inequality  RANK  Trees  Eigenvalues  Graphs  Mathematical analysis  Matrix methods  Eigen values
Journal Article
Bulletin of the Malaysian Mathematical Sciences Society, ISSN 21804206, 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–Gaddumtype inequalities  Distance signless Laplacian matrix  Mathematics, general  Mathematics  Applications of Mathematics  15A18  MATHEMATICS  MATRIX  WIENER  ENERGY  RADIUS  NordhausGaddumtype inequalities  SHARP BOUNDS  Eigenvalues  Lower bounds  Graphs  Graph theory
05C12  Line graph  05C50  Spectral radius  Transmission regular  Nordhaus–Gaddumtype inequalities  Distance signless Laplacian matrix  Mathematics, general  Mathematics  Applications of Mathematics  15A18  MATHEMATICS  MATRIX  WIENER  ENERGY  RADIUS  NordhausGaddumtype inequalities  SHARP BOUNDS  Eigenvalues  Lower bounds  Graphs  Graph theory
Journal Article
Bulletin of the Malaysian Mathematical Sciences Society, ISSN 01266705, 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  kdomination  MATHEMATICS  NUMBERS  NordhausGaddum  Minimum weight  Mathematical functions  Graph theory
05C20  Nordhaus–Gaddum  Signed domination  Double Roman domination  Mathematics, general  Roman domination  Mathematics  Applications of Mathematics  Digraph  05C69  k domination  kdomination  MATHEMATICS  NUMBERS  NordhausGaddum  Minimum weight  Mathematical functions  Graph theory
Journal Article
Bulletin of the Malaysian Mathematical Sciences Society, ISSN 01266705, 7/2018, Volume 41, Issue 3, pp. 1199  1209
A path P in an edgecolored 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–Gaddumtype  Proper connection number  05C35  Diameter  05C38  MATHEMATICS  NordhausGaddumtype  RAINBOW CONNECTION  Graphs  Graph theory  Graph coloring  Upper bounds
Proper path  05C50  Complement graph  05C40  Mathematics  15A18  92E10  Mathematics, general  Applications of Mathematics  Nordhaus–Gaddumtype  Proper connection number  05C35  Diameter  05C38  MATHEMATICS  NordhausGaddumtype  RAINBOW CONNECTION  Graphs  Graph theory  Graph coloring  Upper bounds
Journal Article
Discrete mathematics, ISSN 0012365X, 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 nonzero Laplacian eigenvalues of a graph G. In this paper, we first obtain sharp...
Laplacianenergylike invariant  Kirchhoff index  Nordhaus–Gaddumtype  Laplacian eigenvalues  Matching number  NordhausGaddumtype  MATHEMATICS  ENERGYLIKE INVARIANT  CONNECTIVITY
Laplacianenergylike invariant  Kirchhoff index  Nordhaus–Gaddumtype  Laplacian eigenvalues  Matching number  NordhausGaddumtype  MATHEMATICS  ENERGYLIKE INVARIANT  CONNECTIVITY
Journal Article
Journal of combinatorial optimization, ISSN 15732886, 2017, Volume 35, Issue 1, pp. 126  133
A Nordhaus–Gaddumtype result is a lower or an upper bound on the sum or the product of a parameter of a graph and its complement. In this paper we continue...
Total Roman domination number  Nordhaus–Gaddum inequalities  Convex and Discrete Geometry  Operations Research/Decision Theory  Mathematics  Theory of Computation  Total Roman dominating function  Mathematical Modeling and Industrial Mathematics  Combinatorics  Optimization  MATHEMATICS, APPLIED  COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS  NordhausGaddum inequalities  GRAPHS
Total Roman domination number  Nordhaus–Gaddum inequalities  Convex and Discrete Geometry  Operations Research/Decision Theory  Mathematics  Theory of Computation  Total Roman dominating function  Mathematical Modeling and Industrial Mathematics  Combinatorics  Optimization  MATHEMATICS, APPLIED  COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS  NordhausGaddum inequalities  GRAPHS
Journal Article
Bulletin of the Malaysian Mathematical Sciences Society, ISSN 01266705, 1/2019, Volume 42, Issue 1, pp. 381  390
A graph is said to be totalcolored if all the edges and the vertices of the graph are colored. A path P in a totalcolored graph G is called a totalproper...
Totalproper connection number  Totalproper path  05C40  Mathematics, general  Mathematics  Applications of Mathematics  Nordhaus–Gaddumtype  Complementary graph  05C35  05C38  05C15  MATHEMATICS  NordhausGaddumtype
Totalproper connection number  Totalproper path  05C40  Mathematics, general  Mathematics  Applications of Mathematics  Nordhaus–Gaddumtype  Complementary graph  05C35  05C38  05C15  MATHEMATICS  NordhausGaddumtype
Journal Article
Discrete mathematics, ISSN 0012365X, 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  NordhausGaddum  MATHEMATICS  restrained  total  domination
Domination  Nordhaus–Gaddum  Restrained  Total  NordhausGaddum  MATHEMATICS  restrained  total  domination
Journal Article
SIAM journal on discrete mathematics, ISSN 10957146, 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  NordhausGaddum inequality  GRAPH  MATHEMATICS, APPLIED  domination  EMPIRE  Lower bounds  Graphs  Labels  Roman  Marking  Mathematical analysis
Domination  Roman domination number  NordhausGaddum inequality  GRAPH  MATHEMATICS, APPLIED  domination  EMPIRE  Lower bounds  Graphs  Labels  Roman  Marking  Mathematical analysis
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 12343099, 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 degreeKirchhoff index  additive degreeKirchhoff index  resistance distance  Kirchhoff index  NordhausGaddumtype result  Nordhausgaddumtype re sult  Resistance distance  Additive degreekirchhoff index  Multiplicative degreekirchhoff index  MATHEMATICS  CYCLICITY  WIENER  LAPLACIAN SPECTRUM
multiplicative degreeKirchhoff index  additive degreeKirchhoff index  resistance distance  Kirchhoff index  NordhausGaddumtype result  Nordhausgaddumtype re sult  Resistance distance  Additive degreekirchhoff index  Multiplicative degreekirchhoff index  MATHEMATICS  CYCLICITY  WIENER  LAPLACIAN SPECTRUM
Journal Article
Results in Mathematics, ISSN 14226383, 9/2016, Volume 70, Issue 1, pp. 173  182
A vertexcolored 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  Vertexcoloring  total rainbow connected  trianglefree  totalcoloring  complementary graph  Mathematics, general  Nordhaus–Gaddumtype  vertex rainbow path  05C15  NordhausGaddumtype  MATHEMATICS, APPLIED  MATHEMATICS  VERTEXCONNECTION  COMPLEXITY
total rainbow path  rainbow vertex connected  05C40  Mathematics  Vertexcoloring  total rainbow connected  trianglefree  totalcoloring  complementary graph  Mathematics, general  Nordhaus–Gaddumtype  vertex rainbow path  05C15  NordhausGaddumtype  MATHEMATICS, APPLIED  MATHEMATICS  VERTEXCONNECTION  COMPLEXITY
Journal Article
Journal of Combinatorial Optimization, ISSN 13826905, 5/2017, Volume 33, Issue 4, pp. 1443  1453
A tree T in an edgecolored (vertexcolored) graph H is called a monochromatic (vertexmonochromatic) tree if all the edges (internal vertices) of T have the...
68Q25  68Q17  05C40  Mathematics  Theory of Computation  NPcomplete  k Monochromatic vertexindex  Optimization  Convex and Discrete Geometry  k Monochromatic index  Mathematical Modeling and Industrial Mathematics  Operation Research/Decision Theory  Combinatorics  68R10  Nordhaus–Gaddumtype result  05C15  kMonochromatic index  kMonochromatic vertexindex  MATHEMATICS, APPLIED  COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS  NordhausGaddumtype result
68Q25  68Q17  05C40  Mathematics  Theory of Computation  NPcomplete  k Monochromatic vertexindex  Optimization  Convex and Discrete Geometry  k Monochromatic index  Mathematical Modeling and Industrial Mathematics  Operation Research/Decision Theory  Combinatorics  68R10  Nordhaus–Gaddumtype result  05C15  kMonochromatic index  kMonochromatic vertexindex  MATHEMATICS, APPLIED  COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS  NordhausGaddumtype result
Journal Article
Discrete mathematics, algorithms, and applications, ISSN 17938309, 04/2017, Volume 9, Issue 2
Journal Article
Applied mathematics and computation, ISSN 00963003, 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  NordhausGaddum type problem
Double Roman domination  Nordhaus–Gaddum type problem  Algorithm  Cograph  Double Roman domination number  MATHEMATICS, APPLIED  NordhausGaddum type problem
Journal Article
Discrete mathematics, ISSN 0012365X, 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  NordhausGaddum type problem  MATHEMATICS  EDGES  NETWORK RELIABILITY  GRAPHS
Eigenvalue  Nordhaus–Gaddum type problem  Spectral radius  NordhausGaddum type problem  MATHEMATICS  EDGES  NETWORK RELIABILITY  GRAPHS
Journal Article
Applied mathematics and computation, ISSN 00963003, 01/2020, Volume 365
For a real number α ∈ [0, 1], the Aαmatrix 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...
Aαmatrix  Nordhaus–Gaddum  Spectral radius
Aαmatrix  Nordhaus–Gaddum  Spectral radius
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 12343099, 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  NordhausGaddum  Digraph  Domination number  MATHEMATICS  NUMBERS  STRONG EQUALITY
05C20  domination number  Roman domination number  05C69  digraph  NordhausGaddum  Digraph  Domination number  MATHEMATICS  NUMBERS  STRONG EQUALITY
Journal Article
Discrete Applied Mathematics, ISSN 0166218X, 2019, Volume 255, pp. 167  182
An edgecolored graph G is conflictfree connected if, between each pair of distinct vertices of G, there exists a path in G containing a color used on exactly...
Edgecoloring  Conflictfree connection number  Connectivity  Nordhaus–Gaddumtype result  MATHEMATICS, APPLIED  FREE COLORINGS  THEOREM  UNIQUEMAXIMUM  REGIONS  NordhausGaddumtype result  NORDHAUSGADDUM INEQUALITIES  Lower bounds  Graphs  Trees (mathematics)  Graph theory  Graph coloring  Apexes
Edgecoloring  Conflictfree connection number  Connectivity  Nordhaus–Gaddumtype result  MATHEMATICS, APPLIED  FREE COLORINGS  THEOREM  UNIQUEMAXIMUM  REGIONS  NordhausGaddumtype result  NORDHAUSGADDUM INEQUALITIES  Lower bounds  Graphs  Trees (mathematics)  Graph theory  Graph coloring  Apexes
Journal Article
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