Total edge irregularity strength of book graphs and double book graphs

Ratnasari, Lucia; Wahyuni, Sri; Susanti, Yeni; Palupi, Tantri

doi:10.1063/1.5139139

Cited by 4 publications

(2 citation statements)

References 11 publications

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“…Meanwhile, research on the tes cyclic graphs for various graph classes is still being done. Some results of the investigation of tes for some cyclic graphs, including some book graphs, have been determined and can be seen in (Jendrol et al, 2007), (Nurdin et al, 2008), (Chunling et al, 2009), (Ahmad et al, 2014), (Bača and Siddiqui, 2014), (Indriati et al, 2015), (Jayanthi and Sudha, 2015), (Siddiqui et al, 2017), (Putra and Susanti, 2018), (Ratnasari and Susanti, 2018), (Ratnasari et al, 2019), (Susanti et al, 2020).…”

Section: Introductionmentioning

confidence: 99%

Total Edge Irregularity Strength of q Tuple Book Graphs

Ratnasari¹,

Wahyuni²,

Susanti³

et al. 2021

JMR

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Let G(V, E) be a simple, undirected, and finite graph with a vertex set V and an edge set E. An edge irregular total k-labelling is a function f from the set V \cup E to the set of non-negative integer set (1, 2, ... , k) such that any two different edges in E have distinct weights. The weight of edge xy is defined as the sum of the label of vertex x, the label of vertex y and the label of edge xy. The minimum k for which the graph G can be labelled by an edge irregular total k-labelling is called the total edge irregularity strength of G, denoted by tes(G). We have constructed the formula of an edge irregular total k-labelling and determined the total edge irregularity strength of triple book graphs, quadruplet book graphs and quintuplet book graphs. In this paper, we construct an edge irregular total of k-labelling and show the exact value of the total edge irregularity strength of q tuple book graphs.

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Section: Introductionmentioning

confidence: 99%

Total Edge Irregularity Strength of q Tuple Book Graphs

Ratnasari¹,

Wahyuni²,

Susanti³

et al. 2021

JMR

Self Cite

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show abstract

“…Research on the of cyclic graphs for various graph classes is still being done. Several studies on the exact value of in some cyclic graphs, including some book graphs, have been conducted by [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Total edge irregularity strength of quadruplet and quintuplet book graphs

et al. 2021

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Let G= (V, E) be a finite, simple and undirected graph with a vertex set V and an edge set E. An edge irregular total k-labelling is a function f : V ᴗE → {1,2,…,k} such that for any two different edges xy and x’y’ in E, their weights are distinct. The weight of edge xy is the sum of label of edge xy, labels of vertex x and of vertex y. The minimum k for which the graph G admits an edge irregular total k-labelling is called the total edge irregularity strength of G, denoted by tes(G). We have determined the total edge irregularity strength of book graphs, double book graphs and triple book graphs. In this paper, we show the exact value of the total edge irregularity strength of quadruplet book graphs and quintuplet book graphs.

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