3-Vertex friendly index sets of operations of two graphs

Devadas C. Nayak; K. P. Girija; Sabitha D'Souza; Nagarjun Prabhu; Pradeep G. Bhat

doi:10.1016/j.matpr.2023.05.381

3-Vertex friendly index sets of operations of two graphs

Devadas C. Nayak
, K. P. Girija^*
, Sabitha D'Souza
, Nagarjun Prabhu
, Pradeep G. Bhat

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › peer-review

Abstract

The process of assigning integer values either to vertices or edges of a graph is known as graph labeling. A mapping f: V(G) ! f0; 1; 2g is called ternary vertex labeling and f (v) represents the vertex label for v. The set FI₃v (G) ¼ f¹¹e_f * (i) ― e_f * ðjÞ¹¹ : f ^* runs over all 3-vertex friendly labeling f for all i; j 2 f0; 1; 2gg is referred as 3-vertex friendly index set. In order to achieve FI₃v (G), number of vertices are partitioned into fV₀; V₁; V₂g such that ¹¹jV_ij ― ¹¹V_j¹¹¹¹ ≤ 1 for all i; j ¼ 0; 1; 2 with i–j and label the edge uv by jf (u) ― f (v)j where f (u); f (v) 2 f0; 1; 2g: A study of 3-vertex friendly index sets of operations of two graphs such as union, join and cartesian product are presented in this paper.

Original language	English
Pages (from-to)	118-123
Number of pages	6
Journal	Materials Today: Proceedings
Volume	100
DOIs	https://doi.org/10.1016/j.matpr.2023.05.381
Publication status	Published - 2023
Event	2nd International Conference on Materials Science and Mathematics for Advanced Technology, MSMAT 2022 - Virtual, Online, India Duration: 19-12-2023 → 20-12-2023

All Science Journal Classification (ASJC) codes

General Materials Science

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10.1016/j.matpr.2023.05.381

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@article{dc6e601ea1a447a5851f2dee21ce8831,

title = "3-Vertex friendly index sets of operations of two graphs",

abstract = "The process of assigning integer values either to vertices or edges of a graph is known as graph labeling. A mapping f: V(G) ! f0; 1; 2g is called ternary vertex labeling and f (v) represents the vertex label for v. The set FI3v (G) ¼ f11ef * (i) ― ef * {\dh}j{\TH}11 : f * runs over all 3-vertex friendly labeling f for all i; j 2 f0; 1; 2gg is referred as 3-vertex friendly index set. In order to achieve FI3v (G), number of vertices are partitioned into fV0; V1; V2g such that 11jVij ― 11Vj1111 ≤ 1 for all i; j ¼ 0; 1; 2 with i–j and label the edge uv by jf (u) ― f (v)j where f (u); f (v) 2 f0; 1; 2g: A study of 3-vertex friendly index sets of operations of two graphs such as union, join and cartesian product are presented in this paper.",

author = "Nayak, \{Devadas C.\} and Girija, \{K. P.\} and Sabitha D'Souza and Nagarjun Prabhu and Bhat, \{Pradeep G.\}",

note = "Publisher Copyright: {\textcopyright} 2023 Elsevier Ltd. All rights reserved.; 2nd International Conference on Materials Science and Mathematics for Advanced Technology, MSMAT 2022 ; Conference date: 19-12-2023 Through 20-12-2023",

year = "2023",

doi = "10.1016/j.matpr.2023.05.381",

language = "English",

volume = "100",

pages = "118--123",

journal = "Materials Today: Proceedings",

issn = "2214-7853",

publisher = "Elsevier Ltd",

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TY - JOUR

T1 - 3-Vertex friendly index sets of operations of two graphs

AU - Nayak, Devadas C.

AU - Girija, K. P.

AU - D'Souza, Sabitha

AU - Prabhu, Nagarjun

AU - Bhat, Pradeep G.

PY - 2023

Y1 - 2023

N2 - The process of assigning integer values either to vertices or edges of a graph is known as graph labeling. A mapping f: V(G) ! f0; 1; 2g is called ternary vertex labeling and f (v) represents the vertex label for v. The set FI3v (G) ¼ f11ef * (i) ― ef * ðjÞ11 : f * runs over all 3-vertex friendly labeling f for all i; j 2 f0; 1; 2gg is referred as 3-vertex friendly index set. In order to achieve FI3v (G), number of vertices are partitioned into fV0; V1; V2g such that 11jVij ― 11Vj1111 ≤ 1 for all i; j ¼ 0; 1; 2 with i–j and label the edge uv by jf (u) ― f (v)j where f (u); f (v) 2 f0; 1; 2g: A study of 3-vertex friendly index sets of operations of two graphs such as union, join and cartesian product are presented in this paper.

AB - The process of assigning integer values either to vertices or edges of a graph is known as graph labeling. A mapping f: V(G) ! f0; 1; 2g is called ternary vertex labeling and f (v) represents the vertex label for v. The set FI3v (G) ¼ f11ef * (i) ― ef * ðjÞ11 : f * runs over all 3-vertex friendly labeling f for all i; j 2 f0; 1; 2gg is referred as 3-vertex friendly index set. In order to achieve FI3v (G), number of vertices are partitioned into fV0; V1; V2g such that 11jVij ― 11Vj1111 ≤ 1 for all i; j ¼ 0; 1; 2 with i–j and label the edge uv by jf (u) ― f (v)j where f (u); f (v) 2 f0; 1; 2g: A study of 3-vertex friendly index sets of operations of two graphs such as union, join and cartesian product are presented in this paper.

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U2 - 10.1016/j.matpr.2023.05.381

DO - 10.1016/j.matpr.2023.05.381

M3 - Conference article

AN - SCOPUS:85214245176

SN - 2214-7853

VL - 100

SP - 118

EP - 123

JO - Materials Today: Proceedings

JF - Materials Today: Proceedings

T2 - 2nd International Conference on Materials Science and Mathematics for Advanced Technology, MSMAT 2022

Y2 - 19 December 2023 through 20 December 2023

ER -

3-Vertex friendly index sets of operations of two graphs

Abstract

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