Entire Labeling of Plane Graphs

Bača, Martin; Jendroī, Stanislav; Kathiresan, K.; Muthugurupackiam, Kadarkarai

doi:10.12785/amis/010132

Cited by 2 publications

(3 citation statements)

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“…For = 1, it is a direct consequence from Theorem B with the same reason as in the result above. ∎ This lower bound is tight for ladder graphs and its variation and wheels given in [8].…”

Section: Resultsmentioning

confidence: 91%

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The Entire Face Irregularity Strength of a Book With Polygonal Pages

Tilukay

Ilwaru

2015

BAREKENG: J. Mat. & Ter.

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A face irregular entire labeling is introduced by Baca et al. recently, as a modification of the well-known vertex irregular and edge irregular total labeling of graphs and the idea of the entire colouring of plane graph. A face irregular entire k-labeling : ∪ ∪ → {1, 2, ⋯ , } of a 2-connected plane graph = ( , , ) is a labeling of vertices, edges, and faces of such that for any two different faces and , their weights ( ) and ( ) are distinct. The minimum for which a plane graph has a face irregular entire -labeling is called the entire face irregularity strength of , denoted by ( ).This paper deals with the entire face irregularity strength of a book with -polygonal pages, where embedded in a plane as a closed book with −sided external face. AbstrakPelabelan tak teratur seluruh muka diperkenalkan oleh Baca et al. baru-baru ini, sebagai suatu modifikasi atas pelabelan total tak teratur titik dan tak teratur sisi suatu graf serta ide tentang pewarnaan lengkap pada graf bidang. Pelabelan -tak teratur seluruh muka : ∪ ∪ → {1, 2, ⋯ , } dari suatu graf bidang 2-connected = ( , , ) adalah suatu pelabelan seluruh titik, sisi, dan muka internal dari sedemikian sehingga untuk sebarang dua muka and berbeda, bobot muka ( ) and ( ) juga berbeda. Bilangan bulat terkecil sedemikian sehingga suatu graf bidang memiliki suatu pelabelan -tak teratur seluruh muka disebut nilai ketakteraturan seluruh muka dari , dinotasikan oleh ( ).Kami menentukan nilai eksak dari nilai ketakteraturan seluruh muka graf buku segi-, dimana pada bidang datar dapat digambarkan seperti suatu buku tertutup.Kata Kunci: Graf bidang, graf buku segi-, nilai ketakteraturan seluruh muka, pelabelan lengkap -tak teratur muka.

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“…For = 1, it is a direct consequence from Theorem B with the same reason as in the result above. ∎ This lower bound is tight for ladder graphs and its variation and wheels given in [8].…”

Section: Resultsmentioning

confidence: 91%

“…Motivated by this graphs invariants, Baca et al in [8] studied irregular labeling of a plane graph by labeling vertices, edges, and faces then considering the weights of faces. They defined a face irregular entire labeling.…”

Section: Introductionmentioning

confidence: 99%

The Entire Face Irregularity Strength of a Book With Polygonal Pages

Tilukay

Ilwaru

2015

BAREKENG: J. Mat. & Ter.

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“…Baca et al determined a lower bound for the face irregularity strength of type (α, β, c) when a 2-connected plane graph G has more than one faces of the largest sizes [14,16]. ey presented the following theorem.…”

Section: Introductionmentioning

confidence: 99%

Total Face Irregularity Strength of Grid and Wheel Graph under K-Labeling of Type (1, 1, 0)

Mughal

Jamil

2021

Journal of Mathematics

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In this study, we used grids and wheel graphs G = V , E , F , which are simple, finite, plane, and undirected graphs with V as the vertex set, E as the edge set, and F as the face set. The article addresses the problem to find the face irregularity strength of some families of generalized plane graphs under k -labeling of type α , β , γ . In this labeling, a graph is assigning positive integers to graph vertices, graph edges, or graph faces. A minimum integer k for which a total label of all verteices and edges of a plane graph has distinct face weights is called k -labeling of a graph. The integer k is named as total face irregularity strength of the graph and denoted as tfs G . We also discussed a special case of total face irregularity strength of plane graphs under k -labeling of type (1, 1, 0). The results will be verified by using figures and examples.

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Entire Labeling of Plane Graphs

Cited by 2 publications

References 0 publications

The Entire Face Irregularity Strength of a Book With Polygonal Pages

The Entire Face Irregularity Strength of a Book With Polygonal Pages

Total Face Irregularity Strength of Grid and Wheel Graph under K-Labeling of Type (1, 1, 0)

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