k-PRIME TOTAL LABELING OF GRAPHS

Arockiamary, S. Teresa; Babujee, J. Baskar; Vijayalakshmi, G. Vijayalakshmi

doi:10.17654/0974165822051

Cited by 2 publications

(2 citation statements)

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“…Teresa Arockiamary S and Vijayalakshmi G (3) established the idea of vertex k-prime labeling. For each positive integer k, they proved that triangular snake T n , pentagonal snake mC 5 , nanogonal snake mC 9 , cyclic snakes mC n , corona T n ⊙K 1 , mC 5 ⊙K 1 , mC 9 ⊙K 1 , mC n ⊙K 1 for m > 1 and n ≥ 3, class of planar graphs Pl n are vertex k-prime (3,4) .…”

Section: Introductionmentioning

confidence: 99%

Vertex k-Prime Labeling of Theta Graphs

Arockiamary¹,

Vijayalakshmi²

2023

IJST

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Objectives: To analyse some theta related graphs that admit vertex k-prime labeling for each positive integer k. Methods: In this study, vertices of the graphs are assigned with k, k+1,…,k+|V|-1 such that each pair of labels of adjacent vertices are relatively prime. Justifications for the proof are given. Findings: We examine the theta related graphs such as generalised theta graphs, uniform theta graphs, centralised uniform theta graphs for m = 1 are vertex k-prime. In addition, we introduce another structure of theta graph known as centralised generalised theta graph and show that vertex k-prime labeling exists for the graph. Novelty: Vertex k-prime labeling is a new variant of prime labeling and theta families of graphs exhibiting the labeling is a new finding. Another structure of theta graph known as centralised generalised theta graph is introduced and proved that vertex k-prime labeling exists for the graph.

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Section: Introductionmentioning

confidence: 99%

Vertex k-Prime Labeling of Theta Graphs

Arockiamary¹,

Vijayalakshmi²

2023

IJST

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“…In graph labeling our concept has its origin in lucky labeling (1) and proper lucky labeling (2) was its extension. With add on condition it was named as d-lucky labeling (3,4) . This labeling was studied for various graphs by different authors and it was studied for edges as d-lucky edge labeling (5) .…”

Section: Introductionmentioning

confidence: 99%

d - Lucky Face Labeling of Polytopes

Arockiamary,

Sahayamary

2023

IJST

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Objectives: Our main focus in this study is to apply the concept of d-lucky face labeling to a family of polytopes like D n , S n , T n and U n . Methods: The results were obtained by the method of application of formula to the graphs. Findings: We have found the d-lucky face number and proved the graphs are Euler lucky graphs. Novelty: The concept of d-lucky face labeling and Euler lucky graphs are new findings. The d-lucky face labeling differs from other face labeling by its formula.

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k-PRIME TOTAL LABELING OF GRAPHS

Cited by 2 publications

References 0 publications

Vertex k-Prime Labeling of Theta Graphs

Vertex k-Prime Labeling of Theta Graphs

d - Lucky Face Labeling of Polytopes

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