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.

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

Total Vertex Irregularity Strength of Disjoint Union of Ladder Rung Graph and Disjoint Union of Domino Graph

2020 ◽  
Vol 6 (1) ◽  
pp. 47-51
Author(s):  
Nugroho Arif Sudibyo ◽  
Ardymulya Iswardani ◽  
Yohana Putra Surya Rahmad Hidayat
Keyword(s):  
Disjoint Union ◽  
Graph Labeling ◽  
Irregularity Strength

We investigate a graph labeling called the total vertex irregularity strength (tvs(G)). A tvs(G) is minimum for which graph has a vertex irregular total -labeling. In this paper, we determine the total vertex irregularity strength of disjoint union of ladder rung graph and disjoint union of domino graph.  

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

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

scholarly journals Computing The Irregularity Strength of Planar Graphs

Mathematics ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 150 ◽  
Author(s):  
Hong Yang ◽  
Muhammad Siddiqui ◽  
Muhammad Ibrahim ◽  
Sarfraz Ahmad ◽  
Ali Ahmad
Keyword(s):  
Graph Theory ◽  
Circuit Design ◽  
Planar Graphs ◽  
Coding Theory ◽  
Vital Role ◽  
Graph Labeling ◽  
X Ray Crystallography ◽  
Radar Astronomy ◽  
Base Management ◽  
Irregularity Strength

The field of graph theory plays a vital role in various fields. One of the important areas in graph theory is graph labeling used in many applications such as coding theory, X-ray crystallography, radar, astronomy, circuit design, communication network addressing, and data base management. In this paper, we discuss the totally irregular total k labeling of three planar graphs. If such labeling exists for minimum value of a positive integer k, then this labeling is called totally irregular total k labeling and k is known as the total irregularity strength of a graph G. More preciously, we determine the exact value of the total irregularity strength of three planar graphs.

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 Irregularity and Modular Irregularity Strength of Wheels

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2710
Author(s):  
Martin Bača ◽  
Muhammad Imran ◽  
Andrea Semaničová-Feňovčíková
Keyword(s):  
Simple Graph ◽  
Graph Labeling ◽  
Edge Label ◽  
Labeling Scheme ◽  
Natural Modification ◽  
Maximum Multiplicity ◽  
Irregularity Strength

It is easily observed that the vertices of a simple graph cannot have pairwise distinct degrees. This means that no simple graph of the order of at least two is, in this way, irregular. However, a multigraph can be irregular. Chartrand et al., in 1988, posed the following problem: in a loopless multigraph, how can one determine the fewest parallel edges required to ensure that all vertices have distinct degrees? This problem is known as the graph labeling problem and, for its solution, Chartrand et al. introduced irregular assignments. The irregularity strength of a graph G is known as the maximal edge label used in an irregular assignment, minimized over all irregular assignments. Thus, the irregularity strength of a simple graph G is equal to the smallest maximum multiplicity of an edge of G in order to create an irregular multigraph from G. In the present paper, we show the existence of a required irregular labeling scheme that proves the exact value of the irregularity strength of wheels. Then, we modify this irregular mapping in six cases and obtain labelings that determine the exact value of the modular irregularity strength of wheels as a natural modification of the irregularity strength.

Redox Reactions in Lipid Membranes as a Model for Primordial Energy-Conserving Systems

1997 ◽  
Vol 161 ◽  
pp. 437-442
Author(s):  
Salvatore Di Bernardo ◽  
Romana Fato ◽  
Giorgio Lenaz
Keyword(s):  
Experimental Evidence ◽  
Lipid Membranes ◽  
Energy Supply ◽  
Redox Reactions ◽  
Living Systems ◽  
Asymmetric Distribution ◽  
Conservation Of Energy ◽  
Asymmetrical Distribution ◽  
Energy Conserving ◽  
Living Organisms

AbstractOne of the peculiar aspects of living systems is the production and conservation of energy. This aspect is provided by specialized organelles, such as the mitochondria and chloroplasts, in developed living organisms. In primordial systems lacking specialized enzymatic complexes the energy supply was probably bound to the generation and maintenance of an asymmetric distribution of charged molecules in compartmentalized systems. On the basis of experimental evidence, we suggest that lipophilic quinones were involved in the generation of this asymmetrical distribution of charges through vectorial redox reactions across lipid membranes.

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