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Journal articles on the topic 'Graph covering'

Author: Grafiati

Published: 4 June 2021

Last updated: 17 February 2022

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1

GREEN, EDWARD L., SIBYLLE SCHROLL, and NICOLE SNASHALL. "GROUP ACTIONS AND COVERINGS OF BRAUER GRAPH ALGEBRAS." Glasgow Mathematical Journal 56, no. 2 (August 30, 2013): 439–64. http://dx.doi.org/10.1017/s0017089513000372.

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AbstractWe develop a theory of group actions and coverings on Brauer graphs that parallels the theory of group actions and coverings of algebras. In particular, we show that any Brauer graph can be covered by a tower of coverings of Brauer graphs such that the topmost covering has multiplicity function identically one, no loops, and no multiple edges. Furthermore, we classify the coverings of Brauer graph algebras that are again Brauer graph algebras.

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2

Dogan, Derya, and Pinar Dundar. "The Average Covering Number of a Graph." Journal of Applied Mathematics 2013 (2013): 1–4. http://dx.doi.org/10.1155/2013/849817.

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There are occasions when an average value of a graph parameter gives more useful information than the basic global value. In this paper, we introduce the concept of the average covering number of a graph (the covering number of a graph is the minimum number of vertices in a set with the property that every edge has a vertex in the set). We establish relationships between the average covering number and some other graph parameters, find the extreme values of the average covering number among all graphs of a given order, and find the average covering number for some families of graphs.

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Ciesielski, Krzysztof, and Janusz Pawlikowski. "Small Coverings with Smooth Functions under the Covering Property Axiom." Canadian Journal of Mathematics 57, no. 3 (June 1, 2005): 471–93. http://dx.doi.org/10.4153/cjm-2005-020-8.

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AbstractIn the paper we formulate a Covering Property Axiom, CPAprism, which holds in the iterated perfect set model, and show that it implies the following facts, of which (a) and (b) are the generalizations of results of J. Steprāns.(a) There exists a family ℱ of less than continuummany functions from ℝ to ℝ such that ℝ2 is covered by functions from ℱ, in the sense that for every 〈x, y〉 ∈ ℝ2 there exists an f ∈ ℱ such that either f (x) = y or f (y) = x.(b) For every Borel function f : ℝ → ℝ there exists a family ℱ of less than continuum many “” functions (i.e., differentiable functions with continuous derivatives, where derivative can be infinite) whose graphs cover the graph of f.(c) For every n > 0 and a Dn function f: ℝ → ℝ there exists a family ℱ of less than continuum many Cn functions whose graphs cover the graph of f.We also provide the examples showing that in the above properties the smoothness conditions are the best possible. Parts (b), (c), and the examples are closely related to work of A. Olevskiĭ.

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Pirzadaa, Shariefuddin, Hilal A. Ganieb, and Merajuddin Siddique. "On some covering graphs of a graph." Electronic Journal of Graph Theory and Applications 1, no. 2 (October 8, 2016): 132–47. http://dx.doi.org/10.5614/ejgta.2016.4.2.2.

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5

Erdős, P., and L. Pyber. "Covering a graph by complete bipartite graphs." Discrete Mathematics 170, no. 1-3 (June 1997): 249–51. http://dx.doi.org/10.1016/s0012-365x(96)00124-0.

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6

Kwon, Young Soo, and Jaeun Lee. "Enumerating Abelian Typical Cube-Free Fold Coverings of a Circulant Graph." Algebra Colloquium 27, no. 01 (February 25, 2020): 137–48. http://dx.doi.org/10.1142/s1005386720000127.

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Enumerating the isomorphism or equivalence classes of several types of graph coverings is one of the central research topics in enumerative topological graph theory. A covering projection p from a Cayley graph Cay(Γ, X) onto another Cayley graph Cay(Q, Y) is called typical if the function p : Γ → Q on the vertex sets is a group epimorphism. A typical covering is called abelian (or circulant, respectively) if its covering graph is a Cayley graph on an abelian (or a cyclic, respectively) group. Recently, the equivalence classes of connected abelian typical prime-fold coverings of a circulant graph are enumerated. As a continuation of this work, we enumerate the equivalence classes of connected abelian typical cube-free fold coverings of a circulant graph.

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7

Wang, Shiping, Qingxin Zhu, William Zhu, and Fan Min. "Equivalent Characterizations of Some Graph Problems by Covering-Based Rough Sets." Journal of Applied Mathematics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/519173.

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Covering is a widely used form of data structures. Covering-based rough set theory provides a systematic approach to this data. In this paper, graphs are connected with covering-based rough sets. Specifically, we convert some important concepts in graph theory including vertex covers, independent sets, edge covers, and matchings to ones in covering-based rough sets. At the same time, corresponding problems in graphs are also transformed into ones in covering-based rough sets. For example, finding a minimal edge cover of a graph is translated into finding a minimal general reduct of a covering. The main contributions of this paper are threefold. First, any graph is converted to a covering. Two graphs induce the same covering if and only if they are isomorphic. Second, some new concepts are defined in covering-based rough sets to correspond with ones in graph theory. The upper approximation number is essential to describe these concepts. Finally, from a new viewpoint of covering-based rough sets, the general reduct is defined, and its equivalent characterization for the edge cover is presented. These results show the potential for the connection between covering-based rough sets and graphs.

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8

Ma, Jicheng. "On 3-arc-transitive covers of the dodecahedron graph." Filomat 30, no. 13 (2016): 3493–99. http://dx.doi.org/10.2298/fil1613493m.

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In this paper, the following problem is considered: does there exist a t-arc-transitive regular covering graph of an s-arc-transitive graph for positive integers t greater than s? In order to answer this question, we classify all arc-transitive cyclic regular covers of the dodecahedron graph. Two infinite families of 3-arc-transitive abelian covering graphs are given, which give more specific examples that for an s-arc-transitive graph there exist (s+1)-arc-transitive covering graphs.

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9

Sohn, Moo Young, and Jaeun Lee. "Characteristic polynomials of some weighted graph bundles and its application to links." International Journal of Mathematics and Mathematical Sciences 17, no. 3 (1994): 503–10. http://dx.doi.org/10.1155/s0161171294000748.

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In this paper, we introduce weighted graph bundles and study their characteristic polynomial. In particular, we show that the characteristic polynomial of a weightedK2(K¯2)-bundles over a weighted graphG?can be expressed as a product of characteristic polynomials two weighted graphs whose underlying graphs areGAs an application, we compute the signature of a link whose corresponding weighted graph is a double covering of that of a given link.

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Vasanthi, R., and K. Subramanian. "On Vertex Covering Transversal Domination Number of Regular Graphs." Scientific World Journal 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/1029024.

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A simple graphG=(V,E)is said to ber-regular if each vertex ofGis of degreer. The vertex covering transversal domination numberγvct(G)is the minimum cardinality among all vertex covering transversal dominating sets ofG. In this paper, we analyse this parameter on different kinds of regular graphs especially forQnandH3,n. Also we provide an upper bound forγvctof a connected cubic graph of ordern≥8. Then we try to provide a more stronger relationship betweenγandγvct.

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11

Doğan Durgun, D., and Ali Bagatarhan. "Average covering number for some graphs." RAIRO - Operations Research 53, no. 1 (January 2019): 261–68. http://dx.doi.org/10.1051/ro/2018044.

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The interconnection networks are modeled by means of graphs to determine the reliability and vulnerability. There are lots of parameters that are used to determine vulnerability. The average covering number is one of them which is denoted by $ \overline{\beta }(G)$, where G is simple, connected and undirected graph of order n ≥ 2. In a graph G = (V(G), E(G)) a subset $ {S}_v\subseteq V(G)$ of vertices is called a cover set of G with respect to v or a local covering set of vertex v, if each edge of the graph is incident to at least one vertex of Sv. The local covering number with respect to v is the minimum cardinality of among the Sv sets and denoted by βv. The average covering number of a graph G is defined as β̅(G) = 1/|v(G)| ∑ν∈v(G)βν In this paper, the average covering numbers of kth power of a cycle $ {C}_n^k$ and Pn □ Pm, Pn □ Cm, cartesian product of Pn and Pm, cartesian product of Pn and Cm are given, respectively.

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SUN, YACHYANG, and KOK-HOO YEAP. "EDGE COVERING OF COMPLEX TRIANGLES IN RECTANGULAR DUAL FLOORPLANNING." Journal of Circuits, Systems and Computers 03, no. 03 (September 1993): 721–31. http://dx.doi.org/10.1142/s0218126693000435.

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Rectangular dual graph approach to floorplanning is based on the adjacency graph of the modules in a floorplan. If the input adjacency graph contains a cycle of length three which is not a face (complex triangle), a rectangular floorplan does not exist. Thus, complex triangles have to be eliminated before applying any floorplanning algorithm. This paper shows that the weighted complex triangle elimination problem is NP-complete, even when the input graphs are restricted to 1-level containment. For adjacency graph with 0-level containment, the unweighted problem is optimally solvable in O(c1.5 + n) time where c is the number of complex triangles and n is the number of vertices of the input graph.

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Chandoor, Susanth, and Sunny Joseph Kalayathankal. "Operations on covering numbers of certain graph classes." International Journal of Advanced Mathematical Sciences 4, no. 1 (January 21, 2016): 1. http://dx.doi.org/10.14419/ijams.v4i1.5531.

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<p><span>The bounds on the sum and product of chromatic numbers of a graph and its complement are known as Nordhaus-Gaddum inequalities. In a similar way, the operations on the covering numbers of graphs with their complement are studied and with respect to this, new characterizations of certain graph classes have also been given in this paper.</span></p>

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Li, Jingjian, and Jicheng Ma. "On Pentavalent Arc-Transitive Graphs." Algebra Colloquium 25, no. 02 (May 22, 2018): 189–202. http://dx.doi.org/10.1142/s1005386718000135.

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In this paper, a characterization of all pentavalent arc-transitive graphs is given. It is shown that each pentavalent arc-transitive covering graph Γ is a regular simple or elementary abelian covering graph. In particular, the elementary abelian covering groups are ℤ3, ℤ5 or a subgroup of [Formula: see text].

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15

Alhevaz, Abdollah, Maryam Baghipur, Ebrahim Hashemi, and Yaser Alizadeh. "Minimum covering reciprocal distance signless Laplacian energy of graphs." Acta Universitatis Sapientiae, Informatica 10, no. 2 (December 1, 2018): 218–40. http://dx.doi.org/10.2478/ausi-2018-0011.

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Abstract Let G be a simple connected graph. The reciprocal transmission Tr′G(ν) of a vertex ν is defined as $${\rm{Tr}}_{\rm{G}}^\prime ({\rm{\nu }}) = \sum\limits_{{\rm{u}} \in {\rm{V}}(G)} {{1 \over {{{\rm{d}}_{\rm{G}}}(u,{\rm{\nu }})}}{\rm{u}} \ne {\rm{\nu }}.} $$ The reciprocal distance signless Laplacian (briefly RDSL) matrix of a connected graph G is defined as RQ(G)= diag(Tr′ (G)) + RD(G), where RD(G) is the Harary matrix (reciprocal distance matrix) of G and diag(Tr′ (G)) is the diagonal matrix of the vertex reciprocal transmissions in G. In this paper, we investigate the RDSL spectrum of some classes of graphs that are arisen from graph operations such as cartesian product, extended double cover product and InduBala product. We introduce minimum covering reciprocal distance signless Laplacian matrix (or briey MCRDSL matrix) of G as the square matrix of order n, RQC(G) := (qi;j), $${{\rm{q}}_{{\rm{ij}}}} = \left\{ {\matrix{ {1 + {\rm{Tr}}\prime ({{\rm{\nu }}_{\rm{i}}})} & {{\rm{if}}} & {{\rm{i = j}}} & {{\rm{and}}} & {{{\rm{\nu }}_{\rm{i}}} \in {\rm{C}}} \cr {{\rm{Tr}}\prime ({{\rm{\nu }}_{\rm{i}}})} & {{\rm{if}}} & {{\rm{i = j}}} & {{\rm{and}}} & {{{\rm{\nu }}_{\rm{i}}} \notin {\rm{C}}} \cr {{1 \over {{\rm{d(}}{{\rm{\nu }}_{\rm{i}}},{{\rm{\nu }}_{\rm{j}}})}}} & {{\rm{otherwise}}} & {} & {} & {} \cr } } \right.$$ where C is a minimum vertex cover set of G. MCRDSL energy of a graph G is defined as sum of eigenvalues of RQC. Extremal graphs with respect to MCRDSL energy of graph are characterized. We also obtain some bounds on MCRDSL energy of a graph and MCRDSL spectral radius of 𝒢, which is the largest eigenvalue of the matrix RQC (G) of graphs.

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Li, Qingyin, and William Zhu. "Covering Cycle Matroid." ISRN Applied Mathematics 2013 (June 5, 2013): 1–12. http://dx.doi.org/10.1155/2013/539401.

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Covering is a type of widespread data representation while covering-based rough sets provide an efficient and systematic theory to deal with this type of data. Matroids are based on linear algebra and graph theory and have a variety of applications in many fields. In this paper, we construct two types of covering cycle matroids by a covering and then study the graphical representations of these two types of matriods. First, through defining a cycle graph by a set, the type-1 covering cycle matroid is constructed by a covering. By a dual graph of the cycle graph, the covering can also induce the type-2 covering cycle matroid. Second, some characteristics of these two types of matroids are formulated by a covering, such as independent sets, bases, circuits, and support sets. Third, a coarse covering of a covering is defined to study the graphical representation of the type-1 covering cycle matroid. We prove that the type-1 covering cycle matroid is graphic while the type-2 covering cycle matroid is not always a graphic matroid. Finally, relationships between these two types of matroids and the function matroid are studied. In a word, borrowing from matroids, this work presents an interesting view, graph, to investigate covering-based rough sets.

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17

HAMID, I. SAHUL, and A. ANITHA. "ON THE LABEL GRAPHOIDAL COVERING NUMBER-II." Discrete Mathematics, Algorithms and Applications 03, no. 01 (March 2011): 1–7. http://dx.doi.org/10.1142/s179383091100095x.

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Let G = (V, E) be a graph with p vertices and q edges. An acyclic graphoidal cover of G is a collection ψ of paths in G which are internally disjoint and covering each edge of the graph exactly once. Let f : V → {1, 2, …, p} be a labeling of the vertices of G. Let ↑Gf be the directed graph obtained by orienting the edges uv of G from u to v provided f(u) < f(v). If the set ψf of all maximal directed paths in ↑Gf, with directions ignored, is an acyclic graphoidal cover of G, then f is called a graphoidal labeling of G and G is called a label graphoidal graph and ηl = min {|ψf|: f is a graphoidal labeling of G} is called the label graphoidal covering number of G. An orientation of G in which every vertex of degree greater than 2 is either a sink or a source is a graphoidal orientation. In this paper we characterize graphs for which (i) ηl = ηa and (ii) ηl = Δ. Also, we discuss the relation between graphoidal labeling and graphoidal orientation.

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Dondi, Riccardo, Giancarlo Mauri, Florian Sikora, and Italo Zoppis. "Covering a Graph with Clubs." Journal of Graph Algorithms and Applications 23, no. 2 (2019): 271–92. http://dx.doi.org/10.7155/jgaa.00491.

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19

Labbé, Martine, Gilbert Laporte, and Patrick Soriano. "Covering a graph with cycles." Computers & Operations Research 25, no. 6 (June 1998): 499–504. http://dx.doi.org/10.1016/s0305-0548(97)00082-8.

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20

Jayaram, S. R., and Divya Rashmi S V. "Covering matrices of a graph." International Journal of Mathematics Trends and Technology 46, no. 1 (June 25, 2017): 37–42. http://dx.doi.org/10.14445/22315373/ijmtt-v46p508.

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21

Wang, Hong. "Covering a graph with cycles." Journal of Graph Theory 20, no. 2 (October 1995): 203–11. http://dx.doi.org/10.1002/jgt.3190200209.

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22

Bryant, Roy D., and Harold Fredricksen. "Covering the de Bruijn graph." Discrete Mathematics 89, no. 2 (May 1991): 133–48. http://dx.doi.org/10.1016/0012-365x(91)90362-6.

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23

Khan, Sami Ullah, Abdul Nasir, Naeem Jan, and Zhen-Hua Ma. "Graphical Analysis of Covering and Paired Domination in the Environment of Neutrosophic Information." Mathematical Problems in Engineering 2021 (April 17, 2021): 1–12. http://dx.doi.org/10.1155/2021/5518295.

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Neutrosophic graph (NG) is a powerful tool in graph theory, which is capable of modeling many real-life problems with uncertainty due to unclear, varying, and indeterminate information. Meanwhile, the fuzzy graphs (FGs) and intuitionistic fuzzy graphs (IFGs) may not handle these problems as efficiently as NGs. It is difficult to model uncertainty due to imprecise information and vagueness in real-world scenarios. Many real-life optimization problems are modeled and solved using the well-known fuzzy graph theory. The concepts of covering, matching, and paired domination play a major role in theoretical and applied neutrosophic environments of graph theory. Henceforth, the current study covers this void by introducing the notions of covering, matching, and paired domination in single-valued neutrosophic graph (SVNG) using the strong edges. Also, many attention-grabbing properties of these concepts are studied. Moreover, the strong covering number, strong matching number, and the strong paired domination number of complete SVNG, complete single-valued neutrosophic cycle (SVNC), and complete bipartite SVNG are worked out along with their fascinating properties.

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24

AbuHijleh, Eman, Mohammad Abudayah, Omar Alomari, and Hasan Al-Ezeh. "Matching Number, Independence Number, and Covering Vertex Number of Γ(Zn)." Mathematics 7, no. 1 (January 6, 2019): 49. http://dx.doi.org/10.3390/math7010049.

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Graph invariants are the properties of graphs that do not change under graph isomorphisms, the independent set decision problem, vertex covering problem, and matching number problem are known to be NP-Hard, and hence it is not believed that there are efficient algorithms for solving them. In this paper, the graph invariants matching number, vertex covering number, and independence number for the zero-divisor graph over the rings Z p k and Z p k q r are determined in terms of the sets S p i and S p i q j respectively. Accordingly, a formula in terms of p , q , k , and r, with n = p k , n = p k q r is provided.

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25

MATSUMOTO, KENGO. "FACTOR MAPS OF LAMBDA-GRAPH SYSTEMS AND INCLUSIONS OF C*-ALGEBRAS." International Journal of Mathematics 15, no. 04 (June 2004): 313–39. http://dx.doi.org/10.1142/s0129167x04002351.

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A λ-graph system is a labeled Bratteli diagram with shift transformation. It is a generalization of finite labeled graphs and presents a subshift. In [Doc. Math. 7 (2002), 1–30], the author introduced a C*-algebra [Formula: see text] associated with a λ-graph system [Formula: see text] as a generalization of the Cuntz–Krieger algebras. In this paper, we study a functorial property between factor maps of λ-graph systems and inclusions of the associated C*-algebras with gauge actions. We prove that if there exists a surjective left-covering λ-graph system homomorphism [Formula: see text], there exists a unital embedding of the C*-algebra [Formula: see text] into the C*-algebra [Formula: see text] compatible to its gauge actions. We also show that a sequence of left-covering graph homomorphisms of finite labeled graphs gives rise to a λ-graph system such that the associated C*-algebra is an inductive limit of the Cuntz–Krieger algebras for the finite labeled graphs.

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Kwak, Jin Ho, Jang-Ho Chun, and Jaeun Lee. "Enumeration of Regular Graph Coverings Having Finite Abelian Covering Transformation Groups." SIAM Journal on Discrete Mathematics 11, no. 2 (May 1998): 273–85. http://dx.doi.org/10.1137/s0895480196304428.

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Nimbhorkar, Shriram K., and Vidya S. Deshmukh. "Incomparability graphs of dismantable lattices." Asian-European Journal of Mathematics 13, no. 02 (October 31, 2018): 2050034. http://dx.doi.org/10.1142/s1793557120500345.

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We prove some characterizations of the incomparability graphs of some dismantlable lattices. We discuss the realizability of some standard graphs as a graph of a dismantlable lattice. We also find the minimum covering energy of the incomparability graph of some dismantlable lattices.

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Ma, Jicheng. "Arc-transitive abelian regular covering graphs." International Journal of Algebra and Computation 26, no. 07 (November 2016): 1369–93. http://dx.doi.org/10.1142/s0218196716500594.

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A lot of attention has been paid recently to the construction of symmetric covers of symmetric graphs. After a new approach given by Conder and the author [Arc-transitive abelian regular covers of cubic graphs, J. Algebra 387 (2013) 215–242], the group of covering transformations can be extended to more general abelian groups rather than cyclic or elementary abelian groups. In this paper, by using the Conder–Ma approach, we investigate the symmetric covers of 4-valent symmetric graphs. As an application, all the arc-transitive abelian regular covers of the 4-valent complete graph [Formula: see text] which can be obtained by lifting the arc-transitive subgroups of automorphisms [Formula: see text] and [Formula: see text] are classified.

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Mattiro, N., and I. W. Sudarsana. "Pelabelan Selimut Bintang Ajaib Super Pada Graf Bintang." JURNAL ILMIAH MATEMATIKA DAN TERAPAN 18, no. 1 (June 14, 2021): 95–109. http://dx.doi.org/10.22487/2540766x.2021.v18.i1.15479.

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Let be a simple graph. An edge covering of is a family of subgraphs such that each edge of graph belongs to at least one of the , subgraphs. If each is isomorphic with the given graph , then it is said that contains a covering. The graph G contains a covering and the bijectif function is said an the magic labeling of a graph G if for each subgraph of is isomorphic to , so that is a constant. It is said that the graph G has a super magic if in this case, the graph G which can be labeled with magic is called the covering graph magic. A star graph with n points is a graph with points and sides, where point is degree and the other point has degree denoted by . This study aims to determine the presence of covering labeling for the super-magic star on the star graph. The research methodology is literature study. The results show that the star graph for has magic covering labeling with magic constants for all covering is and the super-magic covering labeling with magic constants for all covering is .

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Park, Choonkil, Nasir Shah, Noor Rehman, Abbas Ali, Muhammad Irfan Ali, and Muhammad Shabir. "Soft covering based rough graphs and corresponding decision making." Open Mathematics 17, no. 1 (May 30, 2019): 423–38. http://dx.doi.org/10.1515/math-2019-0033.

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Abstract Soft set theory and rough set theory are two new tools to discuss uncertainty. Graph theory is a nice way to depict certain information. Particularly soft graphs serve the purpose beautifully. In order to discuss uncertainty in soft graphs, some new types of graphs called soft covering based rough graphs are introduced. Several basic properties of these newly defined graphs are explored. Applications of soft covering based rough graphs in decision making can be very fruitful. In this regard an algorithm has been proposed.

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Füredi, Zoltán. "Covering the complete graph by partitions." Discrete Mathematics 75, no. 1-3 (May 1989): 217–26. http://dx.doi.org/10.1016/0012-365x(89)90088-5.

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Tuza, Zsolt. "Covering all cliques of a graph." Discrete Mathematics 86, no. 1-3 (December 1990): 117–26. http://dx.doi.org/10.1016/0012-365x(90)90354-k.

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Suthar, Sheela, and Om Prakash. "Covering of Line Graph of Zero Divisor Graph over Ring." British Journal of Mathematics & Computer Science 5, no. 6 (January 10, 2015): 728–34. http://dx.doi.org/10.9734/bjmcs/2015/14436.

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Rana, Akul, Anita Pal, and Madhumangal Pal. "An Efficient Algorithm to Solve the Conditional Covering Problem on Trapezoid Graphs." ISRN Discrete Mathematics 2011 (November 17, 2011): 1–10. http://dx.doi.org/10.5402/2011/213084.

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Let G=(V,E) be a simple connected undirected graph. Each vertex v∈V has a cost c(v) and provides a positive coverage radius R(v). A distance duv is associated with each edge {u,v}∈E, and d(u,v) is the shortest distance between every pair of vertices u,v∈V. A vertex v can cover all vertices that lie within the distance R(v), except the vertex itself. The conditional covering problem is to minimize the sum of the costs required to cover all the vertices in G. This problem is NP-complete for general graphs, even it remains NP-complete for chordal graphs. In this paper, an O(n2) time algorithm to solve a special case of the problem in a trapezoid graph is proposed, where n is the number of vertices of the graph. In this special case, duv=1 for every edge {u,v}∈E, c(v)=c for every v∈V(G), and R(v)=R, an integer >1, for every v∈V(G). A new data structure on trapezoid graphs is used to solve the problem.

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YUSTER, RAPHAEL. "Independent Transversals and Independent Coverings in Sparse Partite Graphs." Combinatorics, Probability and Computing 6, no. 1 (March 1997): 115–25. http://dx.doi.org/10.1017/s0963548396002763.

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An [n, k, r]-partite graph is a graph whose vertex set, V, can be partitioned into n pairwise-disjoint independent sets, V1, …, Vn, each containing exactly k vertices, and the subgraph induced by Vi ∪ Vj contains exactly r independent edges, for 1 [les ] i < j [les ] n. An independent transversal in an [n, k, r]-partite graph is an independent set, T, consisting of n vertices, one from each Vi. An independent covering is a set of k pairwise-disjoint independent transversals. Let t(k, r) denote the maximal n for which every [n, k, r]-partite graph contains an independent transversal. Let c(k, r) be the maximal n for which every [n, k, r]-partite graph contains an independent covering. We give upper and lower bounds for these parameters. Furthermore, our bounds are constructive. These results improve and generalize previous results of Erdo″s, Gyárfás and Łuczak [5], for the case of graphs.

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Hong, Sungpyo, Jin Ho Kwak, and Jaeun Lee. "Regular graph coverings whose covering transformation groups have the isomorphism extension property." Discrete Mathematics 148, no. 1-3 (January 1996): 85–105. http://dx.doi.org/10.1016/0012-365x(94)00266-l.

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ROSALIA, TIRA CATUR, LUH PUTU IDA HARINI, and KARTIKA SARI. "PELABELAN SELIMUT TOTAL SUPER (a,d)-H ANTIMAGIC PADA GRAPH LOBSTER BERATURAN L_n (q,r)." E-Jurnal Matematika 6, no. 2 (May 31, 2017): 143. http://dx.doi.org/10.24843/mtk.2017.v06.i02.p159.

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Graph labelling is a function that maps graph elements to positive integers. A covering of graph is family subgraph from , for with integer k. Graph admits covering if for every subgraph is isomorphic to a graph . A connected graph is an - antimagic if there are positive integers and bijective function such that there are injective function , defined by with . The purpose of this research is to determine a total super antimagic covering on lobster graph . The method of this research is literature study method. It is obtained that there are a total super antimagic covering for on lobster graph with integer and even number .

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Khmelnitskaya, Anna, Özer Selçuk, and Dolf Talman. "The average covering tree value for directed graph games." Journal of Combinatorial Optimization 39, no. 2 (October 30, 2019): 315–33. http://dx.doi.org/10.1007/s10878-019-00471-5.

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Abstract We introduce a single-valued solution concept, the so-called average covering tree value, for the class of transferable utility games with limited communication structure represented by a directed graph. The solution is the average of the marginal contribution vectors corresponding to all covering trees of the directed graph. The covering trees of a directed graph are those (rooted) trees on the set of players that preserve the dominance relations between the players prescribed by the directed graph. The average covering tree value is component efficient, and under a particular convexity-type condition it is stable. For transferable utility games with complete communication structure the average covering tree value equals to the Shapley value of the game. If the graph is the directed analog of an undirected graph the average covering tree value coincides with the gravity center solution.

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Pandiya Raj, R., and H. P. Patil. "On the total graph of Mycielski graphs, central graphs and their covering numbers." Discussiones Mathematicae Graph Theory 33, no. 2 (2013): 361. http://dx.doi.org/10.7151/dmgt.1670.

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Philipose, Roshan Sara, and Sarasija P.B. "MINIMUM COVERING GUTMAN ENERGY OF A GRAPH." MATTER: International Journal of Science and Technology 5, no. 1 (March 15, 2019): 01–11. http://dx.doi.org/10.20319/mijst.2019.51.0111.

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Bhat, Pradeep G., and Sabitha D'Souza. "Minimum Covering Energy of Binary Labeled Graph." International Journal of Mathematics and Soft Computing 4, no. 2 (July 13, 2014): 153. http://dx.doi.org/10.26708/ijmsc.2014.2.4.16.

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Kanna, M. R. Rajesh, B. N. Dharmendra, and R. Pradeep Kumar. "Minimum covering distance energy of a graph." Applied Mathematical Sciences 7 (2013): 5525–36. http://dx.doi.org/10.12988/ams.2013.38477.

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Kulli, V. R., and R. R. Iyer. "Inverse vertex covering number of a graph." Journal of Discrete Mathematical Sciences and Cryptography 15, no. 6 (December 2012): 389–93. http://dx.doi.org/10.1080/09720529.2012.10698391.

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Naserasr, Reza, and Claude Tardif. "The chromatic covering number of a graph." Journal of Graph Theory 51, no. 3 (March 2006): 199–204. http://dx.doi.org/10.1002/jgt.20127.

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Kanna, M. R. Rajesh, R. Pradeep Kumar, and R. Jagadeesh. "Minimum covering color energy of a graph." International Journal of Mathematical Analysis 9 (2015): 351–64. http://dx.doi.org/10.12988/ijma.2015.412382.

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Wang, Hong. "On Covering a Bipartite Graph with Cycles." SIAM Journal on Discrete Mathematics 15, no. 1 (January 2001): 86–96. http://dx.doi.org/10.1137/s0895480196310487.

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Shimomura, Takashi. "Bratteli–Vershik models and graph covering models." Advances in Mathematics 367 (June 2020): 107127. http://dx.doi.org/10.1016/j.aim.2020.107127.

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Hartman, Alan, and Yoav Medan. "Covering the complete graph with plane cycles." Discrete Applied Mathematics 44, no. 1-3 (July 1993): 305–10. http://dx.doi.org/10.1016/0166-218x(93)90239-k.

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Pretzel, Oliver. "A non-covering graph of girth six." Discrete Mathematics 63, no. 2-3 (1987): 241–44. http://dx.doi.org/10.1016/0012-365x(87)90012-4.

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Corrádi, K., and S. Szabó. "Cube tiling and covering a complete graph." Discrete Mathematics 85, no. 3 (December 1990): 319–21. http://dx.doi.org/10.1016/0012-365x(90)90388-x.

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