On face irregular evaluations of plane graphs

Bača, Martin; Ovais, Ali; Semaničová-Feňovčíková, Andrea; Suparta, I Nengah

doi:10.7151/dmgt.2294

Cited by 4 publications

(4 citation statements)

References 21 publications

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“…Shabbir et al [11] have proved their exact values of the strength of total vertex (edge) irregularities of a randomly convex unions of (3,6)-fullerene graphs. In 2022, Bača et al [12] investigated the irregular labelings with respect to face of plane graphs and have found a new graph characteristic which can be termed as face irregularity strength of a few types ðα; β; γÞ: . Also, Tilukay et al [13] have estimated the bounds of total face irregularity strength tfsðGÞ: and have proved that the lower bound is sharp for G isomorphic to a cycle, a book with m polygonal pages, or a wheel.…”

Section: Introductionmentioning

confidence: 99%

Total Face Irregularity Strength of Certain Graphs

Emilet,

Paul,

Jayagopal

et al. 2024

Mathematical Problems in Engineering

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The edge k-labeling ψ of G is defined by a mapping from EG to a set of integers 1,2,…,k, where the integer weight assigned to the vertex x∈VG is given as wψx=∑ψxy, such that the sum is taken over every vertex of y∈VG that is adjacent to x and the integer weights of adjacent vertices must be distinct for all vertices with x≠y. An irregular assignment of G using atmost k labels which is considered to be a minimum k is defined as irregularity strength of a graph G and can be denoted as sG. There are also further works on familiar irregular assignments, such as edge irregular labelings, vertex irregular total labelings, edge irregular total labelings, and face irregular entire k-labelings of plane graphs. A plane graph can be defined as a graph that is embedded in the plane in which no two lines will be intersected. In a plane graph the number of regions present are called faces and we denote it as F. The concept of total face irregularity strength is defined by the motivation of irregular networks and entire irregular face k-labeling. In our paper, we have obtained a minimum bound for the total face irregularity strength of two-connected plane graphs like cycle-of-ladder, C-necklace graph, P-necklace graph, sibling tree, and triangular graph.

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Section: Introductionmentioning

confidence: 99%

Total Face Irregularity Strength of Certain Graphs

Emilet,

Paul,

Jayagopal

et al. 2024

Mathematical Problems in Engineering

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“…Baca et al determined total irregularity strength of graphs and calculated bounds and exact values for different families of graphs [14]. Baca et al investigated face irregular evaluations of plane graphs and calculated face irregularity strength of type (α, β, c) for ladder graphs [15].…”

Section: Introductionmentioning

confidence: 99%

Total Face Irregularity Strength of Grid and Wheel Graph under K-Labeling of Type (1, 1, 0)

Mughal

Jamil

2021

Journal of Mathematics

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In this study, we used grids and wheel graphs G = V , E , F , which are simple, finite, plane, and undirected graphs with V as the vertex set, E as the edge set, and F as the face set. The article addresses the problem to find the face irregularity strength of some families of generalized plane graphs under k -labeling of type α , β , γ . In this labeling, a graph is assigning positive integers to graph vertices, graph edges, or graph faces. A minimum integer k for which a total label of all verteices and edges of a plane graph has distinct face weights is called k -labeling of a graph. The integer k is named as total face irregularity strength of the graph and denoted as tfs G . We also discussed a special case of total face irregularity strength of plane graphs under k -labeling of type (1, 1, 0). The results will be verified by using figures and examples.

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“…The other possible cases are V (G) ∪ F (G), E(G) ∪ F (G) and V (G) ∪ E(G) ∪ F (G) which are defined as vertex-face k-labeling of type (1, 0, 1), edge-face k-labeling of type (0, 1, 1) and entire k-labeling of type (1, 1, 1) respectively. The trivial case (α, β, γ) = (0, 0, 0) is never allowed [18]. The weight of a vertex is the sum of labels of that vertex itself and the labels of its adjacent edges, the weight of a graph edge is the sum of label of that edge itself and the labels of its adjacent vertices, the weight of a face is the sum of labels of that face itself and the labels of its surrounding edges and vertices.…”

Section: Introductionmentioning

confidence: 99%

“…A detailed concept of face irregular entire labeling as a modification of vertex irregular and edge irregular total labeling of plane graphs can be seen in [17]. Later, in 2020, Baca et al investigated face irregular evaluations of plane graphs and obtained estimations on face irregularity strength of type (α, β, γ) for ladder graphs [18]. This paper, total face irregularity strength of grid graphs under labeling φ of type (α, β, γ) is a modification of face irregular evaluations of plane graphs, referred as [18].…”

Section: Introductionmentioning

confidence: 99%

Total Face Irregularity Strength of Type (Alpha, Beta, Gamma) of Grid Graphs

Mughal¹,

Jamil²

2021

Preprint

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We investigate new graph characteristics namely total (vertex, edge) face irregularity strength of gen- eralized plane grid graphs Gmn under k-labeling Phi of type (Alpha, Beta, Gamma). The minimum integer k for which a vertex-edge labelled graph has distinct face weights is called the total face irregularity strength of the graph and is denoted by tfs(Gmn). In this article, the graphs G = (V;E; F) under consideration are simple, finite, undirected and planar. We will estimate the exact tight lower bounds for the total face irregularity strength of some families of generalized plane grid graphs.

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On face irregular evaluations of plane graphs

Cited by 4 publications

References 21 publications

Total Face Irregularity Strength of Certain Graphs

Total Face Irregularity Strength of Certain Graphs

Total Face Irregularity Strength of Grid and Wheel Graph under K-Labeling of Type (1, 1, 0)

Total Face Irregularity Strength of Type (Alpha, Beta, Gamma) of Grid Graphs

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