scholarly journals Edge Irregular Reflexive Labeling for Disjoint Union of Generalized Petersen Graph

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 304 ◽  
Author(s):  
Juan Guirao ◽  
Sarfraz Ahmad ◽  
Muhammad Siddiqui ◽  
Muhammad Ibrahim
Keyword(s):  
Disjoint Union ◽  
Graph Labeling ◽  
Petersen Graph ◽  
Generalized Petersen Graph ◽  
Whole Numbers ◽  
Labeled Graph ◽  
Edge Strength ◽  
Correct Estimation ◽  
Edge Labeling

A graph labeling is the task of integers, generally spoken to by whole numbers, to the edges or vertices, or both of a graph. Formally, given a graph G = ( V , E ) a vertex labeling is a capacity from V to an arrangement of integers. A graph with such a capacity characterized is known as a vertex-labeled graph. Similarly, an edge labeling is an element of E to an arrangement of labels. For this situation, the graph is called an edge-labeled graph. We examine an edge irregular reflexive k-labeling for the disjoint association of the cycle related graphs and decide the correct estimation of the reflexive edge strength for the disjoint association of s isomorphic duplicates of the cycle related graphs to be specific Generalized Peterson graphs.

scholarly journals Tree-Antimagicness of Web Graphs and Their Disjoint Union

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Zhijun Zhang ◽  
Muhammad Awais Umar ◽  
Xiaojun Ren ◽  
Basharat Rehman Ali ◽  
Mujtaba Hussain ◽  
...  
Keyword(s):  
Graph Theory ◽  
Disjoint Union ◽  
Graph Labeling ◽  
Labeled Graph ◽  
Antimagic Labeling ◽  
Research Article ◽  
Web Graphs ◽  
Vertex Set ◽  
Edge Labeling

In graph theory, the graph labeling is the assignment of labels (represented by integers) to edges and/or vertices of a graph. For a graph G=V,E, with vertex set V and edge set E, a function from V to a set of labels is called a vertex labeling of a graph, and the graph with such a function defined is called a vertex-labeled graph. Similarly, an edge labeling is a function of E to a set of labels, and in this case, the graph is called an edge-labeled graph. In this research article, we focused on studying super ad,d-T4,2-antimagic labeling of web graphs W2,n and isomorphic copies of their disjoint union.

scholarly journals Edge Irregular Reflexive Labeling for the Disjoint Union of Gear Graphs and Prism Graphs

Mathematics ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 142 ◽  
Author(s):  
Xiujun Zhang ◽  
Muhammad Ibrahim ◽  
Syed Bokhary ◽  
Muhammad Siddiqui
Keyword(s):  
Graph Theory ◽  
Disjoint Union ◽  
Edge Strength ◽  
Whole Number ◽  
Marked Graph ◽  
Correct Estimation

In graph theory, a graph is given names—generally a whole number—to edges, vertices, or both in a chart. Formally, given a graph G = ( V , E ) , a vertex naming is a capacity from V to an arrangement of marks. A diagram with such a capacity characterized defined is known as a vertex-marked graph. Similarly, an edge naming is a mapping of an element of E to an arrangement of marks. In this case, the diagram is called an edge-marked graph. We consider an edge irregular reflexive k-labeling for the disjoint association of wheel-related diagrams and deduce the correct estimation of the reflexive edge strength for the disjoint association of m copies of some wheel-related graphs, specifically gear graphs and prism graphs.

Total irregularity strength of disjoint union of isomorphic copies of generalized Petersen graph

2017 ◽  
Vol 09 (06) ◽  
pp. 1750071
Author(s):  
Muhammad Naeem ◽  
Muhammad Kamran Siddiqui
Keyword(s):  
Disjoint Union ◽  
Petersen Graph ◽  
Generalized Petersen Graph ◽  
Irregularity Strength

Let [Formula: see text] be a graph. A total labeling [Formula: see text] is called totally irregular total [Formula: see text]-labeling of [Formula: see text] if every two distinct vertices [Formula: see text] and [Formula: see text] in [Formula: see text] satisfy [Formula: see text] and every two distinct edges [Formula: see text] and [Formula: see text] in [Formula: see text] satisfy [Formula: see text] where [Formula: see text] and [Formula: see text] The minimum [Formula: see text] for which a graph [Formula: see text] has a totally irregular total [Formula: see text]-labeling is called the total irregularity strength of [Formula: see text], denoted by [Formula: see text] In this paper, we determined the total irregularity strength of disjoint union of [Formula: see text] isomorphic copies of generalized Petersen graph.

On cyclic decompositions of the complete graph into the bipartite generalized Petersen graph P(n,3)

2021 ◽  
Vol 344 (5) ◽  
pp. 112339
Author(s):  
Wannasiri Wannasit
Keyword(s):  
Complete Graph ◽  
Petersen Graph ◽  
Generalized Petersen Graph

The Generalized Connectivity of Generalized Petersen Graph

2021 ◽  
Author(s):  
Yuan Si ◽  
Ping Li ◽  
Yuzhi Xiao ◽  
Jinxia Liang
Keyword(s):  
Steiner Trees ◽  
Petersen Graph ◽  
Generalized Petersen Graph ◽  
Edge Disjoint ◽  
Generalized Connectivity ◽  
Vertex Set

For a vertex set [Formula: see text] of [Formula: see text], we use [Formula: see text] to denote the maximum number of edge-disjoint Steiner trees of [Formula: see text] such that any two of such trees intersect in [Formula: see text]. The generalized [Formula: see text]-connectivity of [Formula: see text] is defined as [Formula: see text]. We get that for any generalized Petersen graph [Formula: see text] with [Formula: see text], [Formula: see text] when [Formula: see text]. We give the values of [Formula: see text] for Petersen graph [Formula: see text], where [Formula: see text], and the values of [Formula: see text] for generalized Petersen graph [Formula: see text], where [Formula: see text] and [Formula: see text].

Edge Coloring of the Signed Generalized Petersen Graph

2021 ◽  
Author(s):  
Hongyan Cai ◽  
Qiang Sun ◽  
Guangjun Xu ◽  
Shanshan Zheng
Keyword(s):  
Edge Coloring ◽  
Petersen Graph ◽  
Generalized Petersen Graph

scholarly journals The K -Size Edge Metric Dimension of Graphs

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Tanveer Iqbal ◽  
Muhammad Naeem Azhar ◽  
Syed Ahtsham Ul Haq Bokhary
Keyword(s):  
Bipartite Graph ◽  
Connected Graph ◽  
Complete Bipartite Graph ◽  
Petersen Graph ◽  
Metric Dimension ◽  
Resolving Set ◽  
Generalized Petersen Graph

In this paper, a new concept k -size edge resolving set for a connected graph G in the context of resolvability of graphs is defined. Some properties and realizable results on k -size edge resolvability of graphs are studied. The existence of this new parameter in different graphs is investigated, and the k -size edge metric dimension of path, cycle, and complete bipartite graph is computed. It is shown that these families have unbounded k -size edge metric dimension. Furthermore, the k-size edge metric dimension of the graphs Pm □ Pn, Pm □ Cn for m, n ≥ 3 and the generalized Petersen graph is determined. It is shown that these families of graphs have constant k -size edge metric dimension.

scholarly journals Graceful Labeling of Hypertrees

2021 ◽  
Vol 13 (1) ◽  
pp. 28
Author(s):  
H. El-Zohny ◽  
S. Radwan ◽  
S.I. Abo El-Fotooh ◽  
Z. Mohammed
Keyword(s):  
Graph Theory ◽  
Simple Graph ◽  
Graph Labeling ◽  
Graceful Labeling ◽  
Edge Labeling

Graph labeling is considered as one of the most interesting areas in graph theory. A labeling for a simple graph G (numbering or valuation), is an association of non -negative integers to vertices of G  (vertex labeling) or to edges of G  (edge labeling) or both of them. In this paper we study the graceful labeling for the k- uniform hypertree and define a condition for the corresponding tree to be graceful. A k- uniform hypertree is graceful if the minimum difference of vertices’ labels of each edge is distinct and each one is the label of the corresponding edge.

Total Irregularity Strengths of an Arbitrary Disjoint Union of (3,6)- Fullerenes

2020 ◽  
Vol 23 ◽  
Author(s):  
Ayesha Shabbir ◽  
Muhammad Faisal Nadeem ◽  
Mohammad Ovais ◽  
Faraha Ashraf ◽  
Sumiya Nasir
Keyword(s):  
Graph Theory ◽  
Lower Bound ◽  
Coding Theory ◽  
Disjoint Union ◽  
Fullerene Molecule ◽  
Graph Labeling ◽  
Fullerene Graph ◽  
Theoretical Concepts ◽  
Large Numbers ◽  
Fullerene Graphs

Aims and Objective: A fullerene graph is a mathematical model of a fullerene molecule. A fullerene molecule or simply a fullerene is a polyhedral molecule made entirely of carbon atoms other than graphite and diamond. Chemical graph theory is a combination of chemistry and graph theory where graph theoretical concepts used to study physical properties of mathematically modeled chemical compounds. Graph labeling is a vital area of graph theory which has application not only within mathematics but also in computer science, coding theory, medicine, communication networking, chemistry and in many other fields. For example, in chemistry vertex labeling is being used in the constitution of valence isomers and transition labeling to study chemical reaction networks. Method and Results: In terms of graphs vertices represent atoms while edges stand for bonds between atoms. By tvs (tes) we mean the least positive integer for which a graph has a vertex (edge) irregular total labeling such that no two vertices (edges) have same weights. A (3,6)-fullerene graph is a non-classical fullerene whose faces are triangles and hexagons. Here, we study the total vertex (edge) irregularity strength of an arbitrary disjoint union of (3,6)-fullerene graphs and providing their exact values. Conclusion: The lower bound for tvs (tes) depending on the number of vertices, minimum and maximum degree of a graph exists in literature while to get different weights one can use sufficiently large numbers, but it is of no interest. Here, by proving that the lower bound is the upper bound we close the case for (3,6)-fullerene graphs.

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.  

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