scholarly journals On the edge irregularity strength for some classes of plane graphs

2021 ◽  
Vol 6 (3) ◽  
pp. 2724-2731
Author(s):  
Ibrahim Tarawneh ◽  
◽  
Roslan Hasni ◽  
Ali Ahmad ◽  
Muhammad Ahsan Asim ◽  
...  
Keyword(s):  
Plane Graphs ◽  
Irregularity Strength

On entire face irregularity strength of disjoint union of plane graphs

2017 ◽  
Vol 307 ◽  
pp. 232-238 ◽  
Author(s):  
Martin Bača ◽  
Marcela Lascsáková ◽  
Maria Naseem ◽  
Andrea Semaničová-Feňovčíková
Keyword(s):  
Disjoint Union ◽  
Plane Graphs ◽  
Irregularity Strength

scholarly journals H-Irregularity Strengths of Plane Graphs

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 229
Author(s):  
Martin Bača ◽  
Nurdin Hinding ◽  
Aisha Javed ◽  
Andrea Semaničová-Feňovčíková
Keyword(s):  
Graph Labeling ◽  
Partial Sums ◽  
Plane Graphs ◽  
Asymmetrical Distribution ◽  
Irregularity Strength

Graph labeling is the mapping of elements of a graph (which can be vertices, edges, faces or a combination) to a set of numbers. The mapping usually produces partial sums (weights) of the labeled elements of the graph, and they often have an asymmetrical distribution. In this paper, we study vertex–face and edge–face labelings of two-connected plane graphs. We introduce two new graph characteristics, namely the vertex–face H-irregularity strength and edge–face H-irregularity strength of plane graphs. Estimations of these characteristics are obtained, and exact values for two families of graphs are determined.

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

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Aleem Mughal ◽  
Noshad Jamil
Keyword(s):  
Plane Graph ◽  
Plane Graphs ◽  
Wheel Graph ◽  
Wheel Graphs ◽  
The Face ◽  
Vertex Set ◽  
Positive Integers ◽  
Special Case ◽  
Irregularity Strength

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.

scholarly journals The total face irregularity strength of some plane graphs

2020 ◽  
Vol 17 (1) ◽  
pp. 495-502
Author(s):  
Meilin I. Tilukay ◽  
A.N.M. Salman ◽  
Venn Y.I. Ilwaru ◽  
F.Y. Rumlawang
Keyword(s):  
Plane Graphs ◽  
Irregularity Strength

Entire H-irregularity Strength of Plane Graphs

2018 ◽  
pp. 3-12
Author(s):  
Martin Bača ◽  
Nurdin Hinding ◽  
Aisha Javed ◽  
Andrea Semaničová-Feňovčíková
Keyword(s):  
Plane Graphs ◽  
Irregularity Strength

scholarly journals The Irregularity and Modular Irregularity Strength of Fan Graphs

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 605
Author(s):  
Martin Bača ◽  
Zuzana Kimáková ◽  
Marcela Lascsáková ◽  
Andrea Semaničová-Feňovčíková
Keyword(s):  
Simple Graph ◽  
Isolated Vertex ◽  
Positive Integers ◽  
Irregularity Strength

For a simple graph G with no isolated edges and at most, one isolated vertex, a labeling φ:E(G)→{1,2,…,k} of positive integers to the edges of G is called irregular if the weights of the vertices, defined as wtφ(v)=∑u∈N(v)φ(uv), are all different. The irregularity strength of a graph G is known as the maximal integer k, minimized over all irregular labelings, and is set to ∞ if no such labeling exists. In this paper, we determine the exact value of the irregularity strength and the modular irregularity strength of fan graphs.

scholarly journals The Matrices of Some of the Plane Graphs and Their Dual

2021 ◽  
Vol 1897 (1) ◽  
pp. 012077
Author(s):  
Rawah A. Zaben ◽  
Israa M. Tawfik
Keyword(s):  
Plane Graphs

scholarly journals Ortho-polygon visibility representations of 3-connected 1-plane graphs

2021 ◽  
Vol 863 ◽  
pp. 40-52
Author(s):  
Giuseppe Liotta ◽  
Fabrizio Montecchiani ◽  
Alessandra Tappini
Keyword(s):  
Plane Graphs ◽  
Visibility Representations
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