TY - JOUR

T1 - Total vertex irregularity strength of generalized prism graphs

AU - Imran, Muhammad

AU - Ahmad, Ali

AU - Siddiqui, Muhammad Kamran

AU - Mehmood, Tariq

N1 - Funding Information:
The research for this article was supported by United Arab Emirates University (UAEU) via Grant No. G00003271.
Publisher Copyright:
© 2022 Taru Publications.

PY - 2022

Y1 - 2022

N2 - A total k-labeling φ : V ∪ E → {1, 2, 3,…, k} is called a vertex irregular total k-labeling, if wt(a) ≠ wt(b), for x ≠ y ∈V, The weight of a vertex is defined as: (Figure presented.), where N(a) is the set of neighbors of a. The minimum value of k for a vertex irregular total k-labeling is called the total vertex irregularity strength of G, tvs(G) [7]. Recently, many authors are studying the two well-known modifications of irregularity strength of graphs, namely, the total edge irregularity strength and the total vertex irregularity strength of graphs. In this paper we study the total vertex irregularity strength of the generalized prism (Figure presented.).

AB - A total k-labeling φ : V ∪ E → {1, 2, 3,…, k} is called a vertex irregular total k-labeling, if wt(a) ≠ wt(b), for x ≠ y ∈V, The weight of a vertex is defined as: (Figure presented.), where N(a) is the set of neighbors of a. The minimum value of k for a vertex irregular total k-labeling is called the total vertex irregularity strength of G, tvs(G) [7]. Recently, many authors are studying the two well-known modifications of irregularity strength of graphs, namely, the total edge irregularity strength and the total vertex irregularity strength of graphs. In this paper we study the total vertex irregularity strength of the generalized prism (Figure presented.).

KW - Generalized prism

KW - Irregularity strength

KW - Primary 05C78

KW - Secondary 05C38

KW - Total vertex irregularity strength

KW - Vertex irregular total k-labeling

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U2 - 10.1080/09720529.2020.1848103

DO - 10.1080/09720529.2020.1848103

M3 - Article

AN - SCOPUS:85099458777

SN - 0972-0529

VL - 25

SP - 1855

EP - 1865

JO - Journal of Discrete Mathematical Sciences and Cryptography

JF - Journal of Discrete Mathematical Sciences and Cryptography

IS - 6

ER -