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Journal of Graph Theory, ISSN 0364-9024, 08/2019, Volume 91, Issue 4, pp. 305 - 325
A graph G is called ( 2 , k )‐connected if G is 2 k‐edge‐connected and G − v is k‐edge‐connected for every vertex v. The study of ( 2 , 2 )‐connected graphs is... 
orientation | splitting‐off | connectivity | connectivity augmentation | splitting-off | MATHEMATICS | 2-CONNECTED ORIENTATIONS | Mathematics | Combinatorics | Computer Science | Discrete Mathematics
Journal Article
IEEE Transactions on Information Theory, ISSN 0018-9448, 11/2017, Volume 63, Issue 11, pp. 7569 - 7574
Let G = (V, E) be a connected undirected graph with k vertices. Suppose that on each vertex of the graph there is a player having an n-bit string. Each player... 
Protocols | Upper bound | Additives | 2-connected graphs | static protocols | Tools | Communication complexity | Electronic mail | equality function | Testing | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Apexes | Graph theory | Number theory
Journal Article
Discrete Mathematics, ISSN 0012-365X, 02/2020, Volume 343, Issue 2, p. 111677
Mader conjectured that for every positive integer k and finite tree T, every k-connected finite graph G with minimum degree δ(G)≥⌊3k2⌋+|T|−1 contains a... 
Connectivity | Caterpillar trees | Isomorphic trees | 2-connected graphs | MATHEMATICS
Journal Article
Discrete Mathematics, ISSN 0012-365X, 10/2013, Volume 313, Issue 19, pp. 1843 - 1855
Let F be a graph and let G, H denote nonempty families of graphs. We write F→(G,H) if in any 2-colouring of edges of  F with red and blue, there is a red... 
2-connected graph | Ramsey minimal graph | Edge colouring | Star | Complete graph | Complete bipartite graph | Cycle | MATHEMATICS | MINIMAL GRAPHS
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 04/2019, Volume 258, pp. 135 - 142
The (ordinary) Wiener index of a connected graph is defined to be the sum of distances between all vertex pairs in this graph. For a connected graph, its... 
2-connected graph | Peripheral Wiener index | Wiener index | Diameter | Bounds | MATHEMATICS, APPLIED | TREES | HARARY INDEX | Trees | Graphs | Trees (mathematics) | Economic impact | Apexes | Upper bounds
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 11/2017, Volume 231, pp. 131 - 138
Given two graphs F and G, an F-WORM coloring of G is an assignment of colors to its vertices in such a way that no F-subgraph of G is monochromatic or rainbow.... 
WORM coloring | Lower chromatic number | 2-connected graphs | Feasible set | Gap in chromatic spectrum | MATHEMATICS, APPLIED
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 02/2020, Volume 40, Issue 1, pp. 51 - 65
A path in a vertex-colored graph is called if there is a color used on exactly one of its vertices. A vertex-colored graph is said to be if any two vertices of... 
2-connected graph | 05C75 | vertex-coloring | 05C40 | tree | conflict-free vertex-connection | 05C15 | MATHEMATICS | 05c75 | 05c40 | 05c15
Journal Article
Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 01/2017, Volume 122, pp. 800 - 814
For graphs G and H, an H-coloring of G is an adjacency preserving map from the vertices of G to the vertices of H. H-colorings generalize such notions as... 
H-coloring | Widom–Rowlinson model | Graph coloring | Graph homomorphisms | London–Hoffman inequality | 2-connected graphs | MATHEMATICS | London Hoffman inequality | Widom Rowlinson model
Journal Article
Discrete Mathematics, ISSN 0012-365X, 07/2019, Volume 342, Issue 7, pp. 2092 - 2099
A graph is minimally 2-(edge)-connected if it is 2-(edge)-connected and deleting any arbitrary chosen edge always leaves a graph which is not... 
Minimally 2-connected graph | Spectral radius | Extremal graph | Minimally 2-edge-connected graph | MATHEMATICS | EIGENVALUES | TREES | CONJECTURES
Journal Article
Discrete Mathematics, ISSN 0012-365X, 04/2018, Volume 341, Issue 4, pp. 1120 - 1124
In Mader (2010), Mader conjectured that for every positive integer k and every finite tree T with order m, every k-connected, finite graph G with... 
Double-stars | 2-Connected graphs | Mader’s conjecture | Stars | Mader's conjecture | MATHEMATICS
Journal Article
SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2012, Volume 26, Issue 1, pp. 193 - 205
A Roman dominating function of a graph G is a function f: V(G) -> {0, 1, 2} such that whenever f(v) = 0, there exists a vertex u adjacent to v such that f(u) =... 
2-connected graph | Domination | Roman domination | MATHEMATICS, APPLIED | domination | EMPIRE | STRATEGY
Journal Article
Discrete Mathematics, ISSN 0012-365X, 09/2014, Volume 330, pp. 17 - 19
A strong edge coloring of a graph G is a proper edge coloring in which every color class is an induced matching. The strong chromatic indexχs′(G) of a graph G... 
Chordless graph | [formula omitted]-degenerate graph | Minimally 2-connected graph | Strong chromatic index | k-degenerate graph | MATHEMATICS
Journal Article
Discrete Mathematics, ISSN 0012-365X, 12/2018, Volume 341, Issue 12, pp. 3500 - 3512
In the last years, connection concepts such as rainbow connection and proper connection appeared in graph theory and received a lot of attention. In this... 
Odd connection | Trees | Edge colouring | Odd vertex-connection | Vertex colouring | 2-connected graphs | MATHEMATICS | PROPER CONNECTION | RAINBOW CONNECTION
Journal Article
Discrete Mathematics, ISSN 0012-365X, 10/2018, Volume 341, Issue 10, pp. 2774 - 2788
In 1962, Erdős proved that if a graph G with n vertices satisfies e(G)>maxn−k2+k2,⌈(n+1)∕2⌉2+n−122,where the minimum degree δ(G)≥k and 1≤k≤(n−1)∕2, then it is... 
Eigenvalues | Claw-free closure | Clique number | Hamilton cycles | Claw-free graph | THEOREM | ANALOGS | PATHS | CLOSURE | ERDOS | MATHEMATICS | 2-CONNECTED GRAPHS | HEAVY SUBGRAPHS | CYCLES | SPECTRAL-RADIUS | BIPARTITE GRAPHS | Mathematics - Combinatorics
Journal Article
Acta Mathematicae Applicatae Sinica, English Series, ISSN 0168-9673, 10/2017, Volume 33, Issue 4, pp. 1001 - 1014
A connected graph G is said to be a factor-critical graph if G −v has a perfect matching for every vertex v of G. In this paper, the 2-connected... 
2-connected graph | Theoretical, Mathematical and Computational Physics | 65D17 | Mathematics | Applications of Mathematics | Math Applications in Computer Science | factor-critical graph | maximum matching | 65D07 | 65D18 | MATHEMATICS, APPLIED
Journal Article
Discrete Mathematics, ISSN 0012-365X, 09/2017, Volume 340, Issue 9, pp. 2217 - 2222
A path in an edge-colored graph is called proper if no two consecutive edges of the path receive the same color. For a connected graph G, the proper connection... 
Proper-path coloring | 2-connected | 3-edge-connected | Proper connection number | Diameter | MATHEMATICS
Journal Article
Journal of Algebra and its Applications, ISSN 0219-4988, 08/2018, Volume 17, Issue 8
Given a graph G, an arithmetical structure on G is a pair of positive integer vectors (d, r) such that gcd(rv vertical bar v is an element of V(G)) = 1 and... 
Arithmetical graphs | 2-connected components | connectivity one | Laplacian matrix | M-matrices | arithmetical structure | cut vertex | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Journal of Combinatorial Optimization, ISSN 1382-6905, 07/2017, Volume 34, Issue 1, pp. 141 - 164
Journal Article
Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 08/2018, Volume 98, Issue 1, pp. 14 - 17
The total distance (orWiener index) of a connected graph G is the sum of all distances between unordered pairs of vertices of G. DeLaVina and Waller ['Spanning... 
diameter | total distance | 2-connected graphs | MATHEMATICS
Journal Article
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