Supermagic coverings of the disjoint union of graphs and amalgamations

Maryati, Tita Khalis; Salman, A. N. M.; Baskoro, Edy Tri

doi:10.1016/j.disc.2012.11.005

Cited by 26 publications

(24 citation statements)

References 6 publications

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“…As a matter of fact, disjoint union of a graph is the relationship between its isomorphic copies keeping the structural properties intact and used to create new larger structures having the same properties as the base graph have. In future, one can extend this idea to find the results for larger differences and for more general structure with applications in theoretical computer science [14][15][16].…”

Section: Resultsmentioning

confidence: 99%

Tree-Antimagicness of Web Graphs and Their Disjoint Union

Zhang

Umar²,

Ren

et al. 2020

Mathematical Problems in Engineering

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In graph theory, the graph labeling is the assignment of labels (represented by integers) to edges and/or vertices of a graph. For a graph G=V,E, with vertex set V and edge set E, a function from V to a set of labels is called a vertex labeling of a graph, and the graph with such a function defined is called a vertex-labeled graph. Similarly, an edge labeling is a function of E to a set of labels, and in this case, the graph is called an edge-labeled graph. In this research article, we focused on studying super ad,d-T4,2-antimagic labeling of web graphs W2,n and isomorphic copies of their disjoint union.

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Section: Resultsmentioning

confidence: 99%

Tree-Antimagicness of Web Graphs and Their Disjoint Union

Zhang

Umar²,

Ren

et al. 2020

Mathematical Problems in Engineering

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“…Ngurah et al [17] proved that chains, wheels, triangles, ladders and grids are cycle-supermagic. Maryati et al [15] investigated the G-supermagicness of a disjoint union of c copies of a graph G and showed that the disjoint union of any paths is cP h -supermagic for some c and h.…”

Section: Introductionmentioning

confidence: 99%

On -Antimagicness of Disconnected Graphs

Bača¹,

Miller

Ryan³

et al. 2016

Bull. Aust. Math. Soc.

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A simple graph $G=(V,E)$ admits an $H$-covering if every edge in $E$ belongs to at least one subgraph of $G$ isomorphic to a given graph $H$. Then the graph $G$ is $(a,d)$-$H$-antimagic if there exists a bijection $f:V\cup E\rightarrow \{1,2,\ldots ,|V|+|E|\}$ such that, for all subgraphs $H^{\prime }$ of $G$ isomorphic to $H$, the $H^{\prime }$-weights, $wt_{f}(H^{\prime })=\sum _{v\in V(H^{\prime })}f(v)+\sum _{e\in E(H^{\prime })}f(e)$, form an arithmetic progression with the initial term $a$ and the common difference $d$. When $f(V)=\{1,2,\ldots ,|V|\}$, then $G$ is said to be super $(a,d)$-$H$-antimagic. In this paper, we study super $(a,d)$-$H$-antimagic labellings of a disjoint union of graphs for $d=|E(H)|-|V(H)|$.

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“…The notion of H-magic graphs was introduced by Gutierrez and Lladó [6] as an extension of the magic valuation given by Kotzig and Rosa [9], which corresponds to the case H = K 2 . Classification studies of H-magic labellings have been intensively investigated (see for example [1][2][3][4][7][8][9][10][11][12][13]). Ahmad et al [1] studied the super K 2 -magicness of an odd union of necessarily nonisomorphic acyclic graphs.…”

Section: Introductionmentioning

confidence: 99%

On Cycle-Supermagicness of Subdivided Graphs

Rizvi

Khalid

Ali

et al. 2015

Bull. Aust. Math. Soc.

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Lladó and Moragas [‘Cycle-magic graphs’, Discrete Math.307 (2007), 2925–2933] showed the cyclic-magic and cyclic-supermagic behaviour of several classes of connected graphs. They discussed cycle-magic labellings of subdivided wheels and friendship graphs, but there are no further results on cycle-magic labellings of other families of subdivided graphs. In this paper, we find cycle-magic labellings for subdivided graphs. We show that if a graph has a cycle-(super)magic labelling, then its uniform subdivided graph also has a cycle-(super)magic labelling. We also discuss some cycle-supermagic labellings for nonuniform subdivided fans and triangular ladders.

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Supermagic coverings of the disjoint union of graphs and amalgamations

Cited by 26 publications

References 6 publications

Tree-Antimagicness of Web Graphs and Their Disjoint Union

Tree-Antimagicness of Web Graphs and Their Disjoint Union

On -Antimagicness of Disconnected Graphs

On Cycle-Supermagicness of Subdivided Graphs

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