On the super edge-magic deficiency of join product and chain graphs

Ngurah, Anak Agung Gede; Simanjuntak, Rinovia

doi:10.5614/ejgta.2019.7.1.12

Cited by 5 publications

(5 citation statements)

References 9 publications

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“…Ngurah and Simanjuntak [21] studied the SEMD of join products of a path, a star, and a cycle, respectively, with isolated vertices. Generally, they showed that the join product of a SEM graph with isolated vertices has finite SEMD.…”

Section: The Semd Of Join Product Of Union Of a Star And A Path With mentioning

confidence: 99%

“…Generally, they showed that the join product of a SEM graph with isolated vertices has finite SEMD. In [22] , the same authors investigated the SEMD of join product of a graph G which has certain properties with an isolated vertex. They gave a necessary condition for

to have zero SEMD as the following lemma.…”

Section: The Semd Of Join Product Of Union Of a Star And A Path With mentioning

confidence: 99%

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On the super edge-magic deficiency of some graphs

Krisnawati

Ngurah

Hidayat

et al. 2020

Heliyon

Self Cite

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Forest with two components 2-regular graph Join product graph A graph is called super edge-magic if there exists a bijection ∶ () ∪ () ⟶ {1, 2, ⋯ , | ()| + | ()|}, where (()) = {1, 2, ⋯ , | ()|}, such that () + () + () is a constant for every edge ∈ (). Such a case, is called a super edge magic labeling of. A bipartite graph with partite sets and is called consecutively super edge-magic if there exists a super edge-magic labeling with the property that () = {1, 2, ⋯ , | |} and () = {| | + 1, | | + 2, ⋯ , | ()|}. The super edge-magic deficiency of a graph , denoted by (), is either the minimum nonnegative integer such that ∪ 1 is super edge-magic or +∞ if there exists no such. The consecutively super edge-magic deficiency of a bipartite graph , denoted by (), is either the minimum nonnegative integer such that ∪ 1 is consecutively super edge-magic or +∞ if there exists no such. In this paper, we study the super edge-magic deficiency of some graphs. We investigate the (consecutively) super edge-magic deficiency of forests with two components. We also investigate the super edge-magic deficiency of a 2-regular graph 2 3 ∪ and join product of 1, ∪ with an isolated vertex.

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Section: The Semd Of Join Product Of Union Of a Star And A Path With mentioning

confidence: 99%

to have zero SEMD as the following lemma.…”

Section: The Semd Of Join Product Of Union Of a Star And A Path With mentioning

confidence: 99%

On the super edge-magic deficiency of some graphs

Krisnawati

Ngurah

Hidayat

et al. 2020

Heliyon

Self Cite

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“…Since then, this theory has been used to describe many fundamental issues or phenomena in operations research, chemistry, computer science, and social science. Numerous groups of authors have introduced and studied various graph generation models from different perspectives [1][2][3][4][5]. Additionally, it has been used in communication roads of cities, city maps, etc.…”

Section: Introductionmentioning

confidence: 99%

Recognizable Languages of k-Forcing Automata

Shamsizadeh,

Zahedi,

Abolpour

et al. 2024

MCA

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In this study, we show that automata theory is also a suitable tool for analyzing a more complex type of the k-forcing process. First, the definition of k-forcing automata is presented according to the definition of k-forcing for graphs. Moreover, we study and discuss the language of k-forcing automata for particular graphs. Also, for some graphs with different k-forcing sets, we study the languages of their k-forcing automata. In addition, for some given recognizable languages, we study the structure of graphs. After that, we show that k-forcing automata arising from isomorph graphs are also isomorph. Also, we present the style of words that can be recognized with k-forcing automata. Moreover, we introduce the structure of graphs the k-forcing automata arising from which recognize some particular languages. To clarify the notions and the results obtained in this study, some examples are submitted as well.

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“…Sugeng and Silaban provide bedge consecutive edge magic total labeling for some classes of regular trees [12] and disconnected graphs [10]. For graphs that don't admit SEMTL, Ngurah and Simanjuntak [7,8] add isolated vertices such that the graph admits SEMTL. The number of isolated vertices added is called the super edge magic deficiency.…”

Section: Introductionmentioning

confidence: 99%

On b-edge consecutive edge magic total labeling on trees

Setiawan

Sugeng

Silaban

2022

EJGTA

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Let G = (V, E) be a simple, connected, and undirected graph, where V and E are the set of vertices and the set of edges of G. An edge magic total labeling on G is a bijection f :Such a labeling is said to be a super edge magic total labeling if f (V ) = {1, 2, . . . , |V |} and a b-edge consecutive edge magic total labeling if f (E) = {b + 1, b + 2, . . . , b + |E|} with b ≥ 1.In this research, we give sufficient conditions for a graph G having a super edge magic total labeling to have a b-edge consecutive edge magic total labeling. We also give several classes of connected graphs which have both labelings.

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On the super edge-magic deficiency of join product and chain graphs

Abstract: A graph G is called super edge-magic if there exists a bijective function

Cited by 5 publications

References 9 publications

On the super edge-magic deficiency of some graphs

On the super edge-magic deficiency of some graphs

Recognizable Languages of k-Forcing Automata

On b-edge consecutive edge magic total labeling on trees

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