On the Total Irregularity Strength of Fan, Wheel, Triangular Book, and Friendship Graphs

Tilukay, Meilin I.; Salman, A. N. M.; Persulessy, Elvinus R.

doi:10.1016/j.procs.2015.12.087

Cited by 19 publications

(15 citation statements)

References 2 publications

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“…Untuk beberapa jenis graf, seperti graf lintasan (path), graf lingkaran (cycle) [5] graf hasil kali kartesius dari beberapa graf [6], graf kipas, graf roda, graf buku segitiga, dan graf persahabatan [7] juga telah ditentukan nilai total tak teratur totalnya. Dalam [7], Tilukay, dkk telah menentukan nilat total ketakteraturan total dari graf kipas, graf roda, graf buku segitiga, dan graf persahabatan, sebagai berikut.…”

Section: Pendahuluanunclassified

Nilai Total Tak Teratur Total Dari Gabungan Terpisah Graf Roda Dan Graf Buku Segitiga

Rahangmetan

Tilukay

Rumlawang

et al. 2015

BAREKENG: J. Mat. & Ter.

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AbstrakPelabelan total tak teratur total yang diperkenalkan oleh Marzuki, dkk merupakan kombinasi dari dua jenis pelabelan tak teratur, yaitu pelabelan total tak teratur titik dan pelabelan total tak teratur titik. Bilangan bulat positif terkecil sedemikian sehingga suatu graf memiliki pelabelan -total tak teratur total disebut nilai total tak teratur total dari , dinotasikan dengan ( ). Pada makalah ini, nilai total tak teratur total dari gabungan terpisah graf roda dan graf buku segitiga ditentukan.Kata Kunci: Pelabelan total tak teratur sisi, pelabelan total tak teratur titik, pelabelan total tak teratur total. AbstractA totally irregular total labeling which had been introduced by Marzuki, et.al is a combination of two types of irregular labeling, edge irregular total labeling and vertex irregular total labeling. The minimum integer for which a graph has a totally irregular total -labeling is called the total irregularity strength of , denoted by ( ). In this paper, we determine the total irregularity strength of disjoint union of wheels and of triangular books.

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Section: Pendahuluanunclassified

Nilai Total Tak Teratur Total Dari Gabungan Terpisah Graf Roda Dan Graf Buku Segitiga

Rahangmetan

Tilukay

Rumlawang

et al. 2015

BAREKENG: J. Mat. & Ter.

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“…Since then, the conjecture has been verified for centralized uniform theta graphs in Putra et al [3], for a polar grid graph in Salama [4], for hexagonal grid graphs in Al-Mushayt et al [5], for Disjoint Union of Wheel Graphs in Jeyanthi [6], for strong product of two paths in Ahmad et al [7], for subdivision of star in Siddiqui [8], for generalized prism in Bača and Siddiqui [9], for helm and sun graphs in Ahmad et al [10], for the corona product of paths with some graphs in Salman and Baskoro [11], for a wheel graph, a fan graph, a triangular Book graph and a friendship graph in Tilukay et al [12], for a categorical product of two paths in Ahmad and Bača [13], for subdivision of star in Hinding et al [14], for series parallel graphs in Rajasingh and Arockiamary [15], for categorical product of two cycles in Ahmad et al [16].…”

Section: Introductionmentioning

confidence: 99%

Computing Total Edge Irregularity Strength for Heptagonal Snake Graph and Related Graphs

Salama

2021

Preprint

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A labeling of edges and vertices of a simple graph 𝐺(𝑉,𝐸) by a mapping Ŧ:𝑉(𝐺) ∪ 𝐸(𝐺)→{ 1,2,3,…,Ћ} provided that any two pair of edges have distinct weights is called an edge irregular total Ћ-labeling. If Ћ is minimum and 𝐺 admits an edge irregular total Ћ -labelling, then Ћ is called the total edge irregularity strength (TEIS) and denoted by 𝑡𝑒𝑠(𝐺). In this paper, the definitions of the heptagonal snake graph HPSn ,the double heptagonal snake graph 𝐷(HPSn) and an 𝑙−multiple heptagonal snake graph 𝐿(HPSn) have been introduced. The exact value of TEISs for the new family has also been investigated.

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“…Combining previous conditions on irregular total labeling, Marzuki et al in [5] defined a totally irregular total labeling. Several upper bounds and exact values of the total irregularity strength of some classes were given in [5][6][7][8], and surveyed in [4].…”

Section: Introductionmentioning

confidence: 99%

The total face irregularity strength of some plane graphs

Tilukay

Salman

Ilwaru

et al. 2020

AKCE International Journal of Graphs and Combinatorics

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A face irregular total k-labeling λ : V ∪ E → {1, 2, . . . , k} of a 2-connected plane graph G is a labeling of vertices and edges such that their face-weights are pairwise distinct. The weight of a face f under a labeling λ is the sum of the labels of all vertices and edges surrounding f . The minimum value k for which G has a face irregular total k-labeling is called the total face irregularity strength of G, denoted by t f s(G). The lower bound of t f s(G) is provided along with the exact value of two certain plane graphs. Improving the results, this paper deals with the total face irregularity strength of the disjoint union of multiple copies of a plane graph G. We estimate the bounds of t f s(G) and prove that the lower bound is sharp for G isomorphic to a cycle, a book with m polygonal pages, or a wheel.

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On the Total Irregularity Strength of Fan, Wheel, Triangular Book, and Friendship Graphs

Cited by 19 publications

References 2 publications

Nilai Total Tak Teratur Total Dari Gabungan Terpisah Graf Roda Dan Graf Buku Segitiga

Nilai Total Tak Teratur Total Dari Gabungan Terpisah Graf Roda Dan Graf Buku Segitiga

Computing Total Edge Irregularity Strength for Heptagonal Snake Graph and Related Graphs

The total face irregularity strength of some plane graphs

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