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Mathematical Proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, 06/2019, pp. 1 - 34
Abstract We analyse the asymptotic extremal growth rate of the Betti numbers of clique complexes of graphs on n vertices not containing a fixed forbidden... 
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 10/2019, Volume 100, Issue 2, pp. 498 - 517
Let Tr(n,m,k) denote the largest number of distinct projections onto k coordinates guaranteed in any family of m binary vectors of length n. The classical... 
05D05 | 68Q01 (secondary) | 52C99 | 05C69 | 68R01 (primary)
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 08/2019, Volume 39, Issue 3, pp. 741 - 755
For a given graph = ( ) and permutation π : ↦ the prism π of is defined as follows: (π ) = ( ) ∪ ( ′), where ′ is a copy of , and ) = ) ∪ ′) ∪ , where = { ′ :... 
prism graphs | 05C69 | domination
Journal Article
Discussiones Mathematicae Graph Theory, 08/2019, Volume 39, Issue 3, pp. 655 - 657
For a graph with vertex set ( ) and independence number ), Selkow [ , Discrete Math. 132 (1994) 363–365] established the famous lower bound on ( ), where ) and... 
05C69 | independence number | graph
Journal Article
Combinatorica, ISSN 0209-9683, 12/2018, Volume 38, Issue 6, pp. 1415 - 1436
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 02/2019, Volume 39, Issue 1, pp. 41 - 53
For a graph G = (V,E), a double Roman dominating function (or just DRDF) is a function f : V → {0, 1, 2, 3} having the property that if f(v) = 0 for a vertex... 
double Roman domination | 05C69 | Roman domination | Double Roman domination | MATHEMATICS
Journal Article
Discussiones Mathematicae Graph Theory, 08/2019, Volume 39, Issue 3, pp. 659 - 671
Let be a graph with vertex set and no isolated vertices. A sub-set ⊆ is a semipaired dominating set of if every vertex in \ is adjacent to a vertex in and can... 
semipaired domination | 05C69 | paired-domination
Journal Article
COMBINATORICA, ISSN 0209-9683, 11/2019, Volume 39, Issue 5, pp. 1173 - 1184
We introduce the asymptotic spectrum of graphs and apply the theory of asymptotic spectra of Strassen (J. Reine Angew. Math. 1988) to obtain a new dual... 
05C76 | MATHEMATICS | LOVASZ | 05C69 | 94C15 | COMPLEXITY
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 08/2017, Volume 96, Issue 1, pp. 47 - 66
We prove tight upper bounds on the logarithmic derivative of the independence and matching polynomials of d‐regular graphs. For independent sets, this theorem... 
05C31 | 05C69 | 05C30 | 82B20 (secondary) | 05C70 (primary) | MATHEMATICS | NUMBER | ENTROPY
Journal Article
Journal of Discrete Mathematical Sciences and Cryptography, ISSN 0972-0529, 07/2019, Volume 22, Issue 5, pp. 761 - 775
Let G = (V, E) be a graph of order n and size m. A set S ⊆ V is a restrained dominating set if every vertex not in S is adjacent to a vertex in S and to a... 
Domination | 11B83 | 05C69 | polynomial | restrained domination
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 08/2018, Volume 38, Issue 3, pp. 703 - 716
We consider γ-graphs, which are reconfiguration graphs of the minimum dominating sets of a graph . We answer three open questions about γ- graphs of trees by... 
05C69 | reconfiguration | domination | Domination, reconfiguration | MATHEMATICS
Journal Article
Quaestiones Mathematicae, ISSN 1607-3606, 10/2014, Volume 37, Issue 4, pp. 547 - 561
For a positive integer b, we define a set S of vertices in a graph G as a b-disjunctive dominating set if every vertex not in S is adjacent to a vertex of S or... 
algorithms | Graph | domination | distance | 05C69 | MATHEMATICS
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 02/2016, Volume 36, Issue 1, pp. 71 - 93
Let be a graph with no isolated vertex. In this paper, we study a parameter that is squeezed between arguably the two most important domination parameters;... 
semitotal domination | domination | 05C69 | trees | Domination | Trees | Semitotal domination | MATHEMATICS | GRAPHS
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 06/2018, Volume 88, Issue 2, pp. 356 - 370
For a maximal outerplanar graph G of order n at least three, Matheson and Tarjan showed that G has domination number at most n/3. Similarly, for a maximal... 
maximal outerplanar graph | domination | 05C69 | total domination | MATHEMATICS
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 02/2020, Volume 40, Issue 1, pp. 355 - 360
We provide a short proof of a conjecture of Davila and Kenter concerning a lower bound on the zero forcing number ) of a graph . More specifically, we show... 
girth | Moore bound | zero forcing | 05C69 | MATHEMATICS | MINIMUM RANK | 05c69 | moore bound
Journal Article
Journal of Information and Optimization Sciences, ISSN 0252-2667, 05/2018, Volume 39, Issue 4, pp. 879 - 887
Let G = (V, E) be a graph. If uv ∈ E, we say that u and v dominate each other. If uv ∈ E and deg u ≥ deg v, we say that u strongly dominates v and v weakly... 
05C69 | Strong and weak cobondage numbers
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 2019, Volume 39, Issue 4, pp. 855 - 856
Let D be a digraph of minimum in-degree at least 1. We prove that for any two natural numbers k, l such that 1 ≤ l ≤ k, the number of (k, l)-kernels of D is... 
05C76 | digraphs | Grundy function | 05C20 | in-domination | kernel | 05C69
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 2019, Volume 39, Issue 4, pp. 841 - 853
A set S of vertices in a graph G is an independent dominating set of G if S is an independent set and every vertex not in S is adjacent to a vertex in S. The... 
independent domination number | 05C10 | cubic graphs | domination number | 05C69
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 2019, Volume 39, Issue 4, pp. 787 - 803
A total Roman dominating function on 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 and the... 
total Roman domination number | 05C69 | total Roman reinforcement number
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 9/2015, Volume 31, Issue 5, pp. 1453 - 1462
In this paper, we continue the study of the domination game in graphs introduced by Brešar et al. (SIAM J Discret Math 24:979–991, 2010). We study the total... 
91A43 | Total domination number | Mathematics | Engineering Design | Combinatorics | 05C69 | 05C57 | Domination game | MATHEMATICS | NUMBER | Graph representations | Graphs
Journal Article
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