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Group distance magic and antimagic graphs

S. Cichacz, D. Froncek, K. Sugeng, Sanming Zhou
2016 Acta Mathematica Sinica. English series  
We prove among other things several general results on group antimagic or magic labellings for Cartesian, direct and strong products of graphs.  ...  As applications we obtain several families of graphs admitting group distance antimagic or magic labellings with respect to elementary Abelian groups, cyclic groups or direct products of such groups.  ...  In Section 3 we study group distance antimagic and magic labellings of Cartesian products of graphs.  ... 
doi:10.1007/s10114-016-4646-9 fatcat:ix5vzm353ndbzjtw325xyj3gwy

Group distance magic and antimagic graphs

S. Cichacz, D. Froncek, K. Sugeng, Sanming Zhou
2015 Electronic Notes in Discrete Mathematics  
We prove among other things several general results on group antimagic or magic labellings for Cartesian, direct and strong products of graphs.  ...  As applications we obtain several families of graphs admitting group distance antimagic or magic labellings with respect to elementary Abelian groups, cyclic groups or direct products of such groups.  ...  In Section 3 we study group distance antimagic and magic labellings of Cartesian products of graphs.  ... 
doi:10.1016/j.endm.2015.05.007 fatcat:xcoiybvmjjcjbabepuzlzd4syu

Some results on (a,d)-distance antimagic labeling

S. K. Patel, Jayesh Vasava
2020 Proyecciones  
With this definition of Cartesian product, we define the book graph B n as the Cartesian product of the star graph S n and the path P 2 and we show that it is not (a, d)-distance antimagic Theorem 4.7.  ...  So H 4 is not (a, 2) distance antimagic. 2 Our next result is about the book graph which is defined with the help of Cartesian product of graphs and so we introduce it here. Definition 4.6.  ...  As d ≤ 2, this inequality does not give any (positive) integer value of a and so K 4¯K1 is not (a, d) distance antimagic.  ... 
doi:10.22199/issn.0717-6279-2020-02-0022 fatcat:rgebptyh4bf6jpg3gsxdtqqgje

On Distance Antimagic Graphs [article]

Rinovia Simanjuntak, Kristiana Wijaya
2013 arXiv   pre-print
Additionally, we study {1}-distance antimagic labelings for some cycle-related connected graphs: cycles, suns, prisms, complete graphs, wheels, fans, and friendship graphs.  ...  For an arbitrary set of distances D⊆{0,1, ..., diam(G)}, a D-weight of a vertex x in a graph G under a vertex labeling f:V→{1,2, ... , v} is defined as w_D(x)=∑_y∈ N_D(x) f(y), where N_D(x) = {y ∈ V| d  ...  Froncek proved that disjoint copies of the Cartesian product of two complete graphs and its complement are (a, 2)-distance antimagic and (a, 1)-distance antimagic, respectively (see [5] and [6] ).  ... 
arXiv:1312.7405v1 fatcat:bmgffc26qfhpbbsi6hcasdsw7q

On Distance Magic Harary Graphs [article]

A V Prajeesh, Krishnan Paramasivam
2018 arXiv   pre-print
This paper establishes two techniques to construct larger distance magic and (a, d)-distance antimagic graphs using Harary graphs and provides a solution to the existence of distance magicness of legicographic  ...  product and direct product of G with C4, for every non-regular distance magic graph G with maximum degree |V(G)|-1.  ...  Problem 1.3. [16] If G is distance antimagic, is it true that the graphs G + K 1 , G + K 2 and the Cartesian product G K 2 are distance antimagic. Lemma 1.3. [17] Let G be an r-regular graph.  ... 
arXiv:1809.07382v1 fatcat:z5pql7lzabdmpcad2izb7wa55q

Orientable Z_n-distance magic regular graphs [article]

Karolina Szopa, Paweł Dyrlaga
2018 arXiv   pre-print
In this paper we provide an infinite family of odd regular graphs possessing an orientable Z_n-distance magic labeling. Our results refer to lexicographic product of graphs.  ...  Hefetz, Mütze, and Schwartz conjectured that every connected undirected graph admits an antimagic orientation. In this paper we support the analogous question for distance magic labeling.  ...  are also very grateful to Dominika Datoń, Kinga Patera, Natalia Pondel, Maciej Gabryś and Przemys law Zietek from "Snark" Research Student Association for their help and involvement in initial phase of  ... 
arXiv:1712.02676v2 fatcat:rfzyr3a64jhztirmnnxs45uopy

Page 7708 of Mathematical Reviews Vol. , Issue 2001K [page]

2001 Mathematical Reviews  
In this paper, the authors study the L(j,k)-labelings of two classes of graphs: Cartesian products of complete graphs and diameter 2 graphs.  ...  products of complete graphs with a condition at distance two.  ... 

Computing Edge Weights of Magic Labeling on Rooted Products of Graphs

Jia-Bao Liu, Hafiz Usman Afzal, Muhammad Javaid
2020 Mathematical Problems in Engineering  
We shall also compute a super a,0 edge-antimagic labeling of rooted product of Pn with a special type of pancyclic graphs.  ...  In this article, we shall compute super a,0 edge-antimagic labeling of the rooted product of Pn and the complete bipartite graph K2,m combined with the union of path, copies of paths, and the star.  ...  In the literature, many results have appeared regarding numeric labelings on several operations of graphs such as graphs obtained from cartesian, corona, rooted, and strong products of various connected  ... 
doi:10.1155/2020/2160104 fatcat:634hpx7qkbhxblkvofjavinpga

On join product and local antimagic chromatic number of regular graphs [article]

Gee-Choon Lau, Wai-Chee Shiu
2022 arXiv   pre-print
Let G = (V,E) be a connected simple graph of order p and size q. A graph G is called local antimagic if G admits a local antimagic labeling. A bijection f : E →{1,2,...  ...  The local antimagic chromatic number, denoted χ_la(G), is the minimum number of induced colors taken over local antimagic labeling of G. Let G and H be two vertex disjoint graphs.  ...  Before the consideration we recall some definitions of famous classes of graphs. The Cartesian product C n ×P 2 is called a prism.  ... 
arXiv:2203.06594v1 fatcat:c6pubs627rghzddu3rxg3pcamu

Harmonious order of graphs

Andrzej Żak
2009 Discrete Mathematics  
We also present some general results concerning harmonious order of the Cartesian product of two given graphs or harmonious order of the disjoint union of copies of a given graph.  ...  Given a graph G = (V , E) and a positive integer t ≥ |E|, a functionh : V (G) → Z t is called a t-harmonious labeling of G ifh is injective for t ≥ |V | or surjective for t < |V |, and h(v) +h(w) =h(x)  ...  The Cartesian graph product G = G 1 G 2 of graphs G 1 and G 2 with disjoint vertex sets V (G 1 ) and V (G 2 ) and edge sets E(G 1 ) and E(G 2 ) is the graph with vertex set V (G 1 )×V (G 2 ) and u = (u  ... 
doi:10.1016/j.disc.2009.05.010 fatcat:xum4y6xnibabfnn2o4tuvtjcta

Orientable Z_n-distance magic graphs

Sylwia Cichacz, Bryan Freyberg, Dalibor Froncek
2018 Discussiones Mathematicae Graph Theory  
Therefore we generalize the notion of distance magic labeling for oriented graphs.  ...  A distance magic labeling of G is a bijection ℓ : V → {1, 2, . . . , n} for which there exists a positive integer k such Tuttes flow conjectures are a major source of inspiration in graph theory.  ...  We recall three graph products (see [12] ). All three, the Cartesian product G H, lexicographic product G • H, direct product G × H are graphs with the vertex set V (G) × V (H).  ... 
doi:10.7151/dmgt.2094 fatcat:qelohan46bd5how4gwlu5q5n4y

Computing Edge Weights of Symmetric Classes of Networks

Hafiz Usman Afzal, Muhammad Javaid, Abdulaziz Mohammed Alanazi, Maryam Gharamah Alshehri, Ali Ahmad
2021 Mathematical Problems in Engineering  
We also provide super a , 0 edge-antimagic labelling of the rooted product of cycle C n and planar pancyclic networks.  ...  Two major classes of such network labellings are magic and antimagic. The notion of super a , 0 edge-antimagic labelling on networks was identified in the late nineties.  ...  of networks). e properties and existence of super (a, d) vertex-antimagic labelling of regular graphs have been discussed in [32] .  ... 
doi:10.1155/2021/5562544 fatcat:cs4f3fvt65hyvfy6fcnpgqwvg4

Zero sum partition into sets of the same order and its applications [article]

Sylwia Cichacz
2017 arXiv   pre-print
We will apply the results to the study of group distance magic graphs as well as to generalized Kotzig arrays.  ...  We will say that an Abelian group Γ of order n has the m-zero-sum-partition property (m-ZSP-property) if m divides n, m≥ 2 and there is a partition of Γ into pairwise disjoint subsets A_1, A_2,... , A_t  ...  The lexicographic product or graph composition G • H of graphs G and H is a graph such that the vertex set of G • H is the Cartesian product V (G) × V (H); and any two vertices (u, v) and (x, y) are adjacent  ... 
arXiv:1702.07859v1 fatcat:hfbnot6f2fdklnsppe2wx56wni

The b-Chromatic Number of Cubic Graphs

Marko Jakovac, Sandi Klavžar
2010 Graphs and Combinatorics  
number of k-independent sets in special graphs.  ...  We prove that a graph with every edge belonging to at most c cycles has game coloring number of at most c + 4.  ...  Keywords: super vertex-antimagic total labeling, vertex-antimagic edge labeling, regular graph.  ... 
doi:10.1007/s00373-010-0898-9 fatcat:5j4t3ji33bbopoker7veh5aybi

Radio labeling for strong product K3 ⊠ Pn

Hengxiao Qi, Saima Nazeer, Imrana Kousar, Muhammad Awais Umar, Nehad Ali Shah
2020 IEEE Access  
The authors are grateful for the valuable comments of the anonymous referees.  ...  Definition 1 . 1 [24] The strong product G H is defined as the union of cartesian product and tensor product of two graph G and H.  ...  In other words, a strong product G H is a graph with 1) the vertex set of the cartesian product V (G) × V (H), and 2) distinct vertices (u, v) and (u , v ) are adjacent in G H iff: a) u = u and vv ∈ E(  ... 
doi:10.1109/access.2020.3002397 fatcat:hlumx3v5hvf2jnyyz74xocemo4
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