Face irregular evaluations of family of grids

Let [Formula: see text] be a connected plane graph. Let [Formula: see text] be a k-labeling where [Formula: see text] and [Formula: see text]. The weight of a face f under ρ is defined as [Formula: see text]. Then ρ is called a face irregular labeling of type [Formula: see text] if [Formula: see tex...

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Bibliographic Details
Published inAKCE international journal of graphs and combinatorics pp. 1 - 16
Main Authors Bayati, Jalal Hatem Hussein, Ovais, Ali, Mahboob, Abid, Rasheed, Muhammad Waheed
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 17.07.2024
Subjects
Cartesian Product of path graphs
Face irregular labeling of type
face irregular strength
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Summary:Let [Formula: see text] be a connected plane graph. Let [Formula: see text] be a k-labeling where [Formula: see text] and [Formula: see text]. The weight of a face f under ρ is defined as [Formula: see text]. Then ρ is called a face irregular labeling of type [Formula: see text] if [Formula: see text] for any two faces [Formula: see text]. The face irregular strength of G is the smallest integer k such that G admits a face irreg ular k-labeling. In this paper we determine the face irregular strength of the grid graph [Formula: see text] under a labeling of type [Formula: see text].
ISSN:0972-8600
2543-3474
DOI:10.1080/09728600.2024.2368126