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Group distance magic and antimagic graphs

2016
*
Acta Mathematica Sinica. English series
*

We prove among other things several general results on group

doi:10.1007/s10114-016-4646-9
fatcat:ix5vzm353ndbzjtw325xyj3gwy
*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*. ...##
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Group distance magic and antimagic graphs

2015
*
Electronic Notes in Discrete Mathematics
*

We prove among other things several general results on group

doi:10.1016/j.endm.2015.05.007
fatcat:xcoiybvmjjcjbabepuzlzd4syu
*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*. ...##
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Some results on (a,d)-distance antimagic labeling

2020
*
Proyecciones
*

With this definition

doi:10.22199/issn.0717-6279-2020-02-0022
fatcat:rgebptyh4bf6jpg3gsxdtqqgje
*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*. ...##
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On Distance Antimagic Graphs
[article]

2013
*
arXiv
*
pre-print

Additionally, we study {1}-

arXiv:1312.7405v1
fatcat:bmgffc26qfhpbbsi6hcasdsw7q
*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] ). ...##
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On Distance Magic Harary Graphs
[article]

2018
*
arXiv
*
pre-print

This paper establishes two techniques to construct larger

arXiv:1809.07382v1
fatcat:z5pql7lzabdmpcad2izb7wa55q
*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*. ...##
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Orientable Z_n-distance magic regular graphs
[article]

2018
*
arXiv
*
pre-print

In this paper we provide an infinite family

arXiv:1712.02676v2
fatcat:rfzyr3a64jhztirmnnxs45uopy
*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*...##
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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. ...##
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Computing Edge Weights of Magic Labeling on Rooted Products of Graphs

2020
*
Mathematical Problems in Engineering
*

We shall also compute a super a,0 edge-

doi:10.1155/2020/2160104
fatcat:634hpx7qkbhxblkvofjavinpga
*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 ...##
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On join product and local antimagic chromatic number of regular graphs
[article]

2022
*
arXiv
*
pre-print

Let G = (V,E) be a connected simple

arXiv:2203.06594v1
fatcat:c6pubs627rghzddu3rxg3pcamu
*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. ...##
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Harmonious order of graphs

2009
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Discrete Mathematics
*

We also present some general results concerning harmonious order

doi:10.1016/j.disc.2009.05.010
fatcat:xum4y6xnibabfnn2o4tuvtjcta
*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 ...##
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Orientable Z_n-distance magic graphs

2018
*
Discussiones Mathematicae Graph Theory
*

Therefore we generalize the notion

doi:10.7151/dmgt.2094
fatcat:qelohan46bd5how4gwlu5q5n4y
*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). ...##
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Computing Edge Weights of Symmetric Classes of Networks

2021
*
Mathematical Problems in Engineering
*

We also provide super a , 0 edge-

doi:10.1155/2021/5562544
fatcat:cs4f3fvt65hyvfy6fcnpgqwvg4
*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] . ...##
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Zero sum partition into sets of the same order and its applications
[article]

2017
*
arXiv
*
pre-print

We will apply the results to the study

arXiv:1702.07859v1
fatcat:hfbnot6f2fdklnsppe2wx56wni
*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 ...##
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The b-Chromatic Number of Cubic Graphs

2010
*
Graphs and Combinatorics
*

number

doi:10.1007/s00373-010-0898-9
fatcat:5j4t3ji33bbopoker7veh5aybi
*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*. ...##
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Radio labeling for strong product K3 ⊠ Pn

2020
*
IEEE Access
*

The authors are grateful for the valuable comments

doi:10.1109/access.2020.3002397
fatcat:hlumx3v5hvf2jnyyz74xocemo4
*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( ...
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