scholarly journals Enumeration of the Edge Weights of Symmetrically Designed Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Muhammad Javaid ◽  
Hafiz Usman Afzal ◽  
Ebenezer Bonyah
Keyword(s):  
Disjoint Union ◽  
Antimagic Labeling ◽  
Pancyclic Graphs

The idea of super a , 0 -edge-antimagic labeling of graphs had been introduced by Enomoto et al. in the late nineties. This article addresses super a , 0 -edge-antimagic labeling of a biparametric family of pancyclic graphs. We also present the aforesaid labeling on the disjoint union of graphs comprising upon copies of C 4 and different trees. Several problems shall also be addressed in this article.

Super face d-antimagic labeling for disjoint union of toroidal fullerenes

2016 ◽  
Vol 55 (3) ◽  
pp. 849-863 ◽  
Author(s):  
Shahid Imran ◽  
Muhammad Hussain ◽  
Muhammad Kamran Siddiqui ◽  
Muhammad Numan
Keyword(s):  
Disjoint Union ◽  
Antimagic Labeling

scholarly journals Computing Edge Weights of Magic Labeling on Rooted Products of Graphs

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Jia-Bao Liu ◽  
Hafiz Usman Afzal ◽  
Muhammad Javaid
Keyword(s):  
Urban Planning ◽  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Data Traffic ◽  
Security Systems ◽  
Diverse Range ◽  
Antimagic Labeling ◽  
Network Engineering ◽  
Pancyclic Graphs

Labeling of graphs with numbers is being explored nowadays due to its diverse range of applications in the fields of civil, software, electrical, and network engineering. For example, in network engineering, any systems interconnected in a network can be converted into a graph and specific numeric labels assigned to the converted graph under certain rules help us in the regulation of data traffic, connectivity, and bandwidth as well as in coding/decoding of signals. Especially, both antimagic and magic graphs serve as models for surveillance or security systems in urban planning. In 1998, Enomoto et al. introduced the notion of super a,0 edge-antimagic labeling of graphs. In this article, we shall compute super a,0 edge-antimagic labeling of the rooted product of Pn and the complete bipartite graph K2,m combined with the union of path, copies of paths, and the star. We shall also compute a super a,0 edge-antimagic labeling of rooted product of Pn with a special type of pancyclic graphs. The labeling provided here will also serve as super a′,2 edge-antimagic labeling of the aforesaid graphs. All the structures discussed in this article are planar. Moreover, our findings have also been illustrated with examples and summarized in the form of a table and 3D plots.

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 Local Antimagic Chromatic Number for Copies of Graphs

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1230
Author(s):  
Martin Bača ◽  
Andrea Semaničová-Feňovčíková ◽  
Tao-Ming Wang
Keyword(s):  
Chromatic Number ◽  
Disjoint Union ◽  
Vertex Coloring ◽  
Vertex Weight ◽  
Antimagic Labeling ◽  
Multiple Copies ◽  
Minimum Number ◽  
Proper Vertex ◽  
Edge Labeling

An edge labeling of a graph G=(V,E) using every label from the set {1,2,⋯,|E(G)|} exactly once is a local antimagic labeling if the vertex-weights are distinct for every pair of neighboring vertices, where a vertex-weight is the sum of labels of all edges incident with that vertex. Any local antimagic labeling induces a proper vertex coloring of G where the color of a vertex is its vertex-weight. This naturally leads to the concept of a local antimagic chromatic number. The local antimagic chromatic number is defined to be the minimum number of colors taken over all colorings of G induced by local antimagic labelings of G. In this paper, we estimate the bounds of the local antimagic chromatic number for disjoint union of multiple copies of a graph.

scholarly journals Another Antimagic Conjecture

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2071
Author(s):  
Rinovia Simanjuntak ◽  
Tamaro Nadeak ◽  
Fuad Yasin ◽  
Kristiana Wijaya ◽  
Nurdin Hinding ◽  
...  
Keyword(s):  
Connected Graph ◽  
Disjoint Union ◽  
Regular Graphs ◽  
Computational Results ◽  
Antimagic Labeling

An antimagic labeling of a graph G is a bijection f:E(G)→{1,…,|E(G)|} such that the weights w(x)=∑y∼xf(y) distinguish all vertices. A well-known conjecture of Hartsfield and Ringel (1990) is that every connected graph other than K2 admits an antimagic labeling. For a set of distances D, a D-antimagic labeling of a graph G is a bijection f:V(G)→{1,…,|V(G)|} such that the weightω(x)=∑y∈ND(x)f(y) is distinct for each vertex x, where ND(x)={y∈V(G)|d(x,y)∈D} is the D-neigbourhood set of a vertex x. If ND(x)=r, for every vertex x in G, a graph G is said to be (D,r)-regular. In this paper, we conjecture that a graph admits a D-antimagic labeling if and only if it does not contain two vertices having the same D-neighborhood set. We also provide evidence that the conjecture is true. We present computational results that, for D={1}, all graphs of order up to 8 concur with the conjecture. We prove that the set of (D,r)-regular D-antimagic graphs is closed under union. We provide examples of disjoint union of symmetric (D,r)-regular that are D-antimagic and examples of disjoint union of non-symmetric non-(D,r)-regular graphs that are D-antimagic. Furthermore, lastly, we show that it is possible to obtain a D-antimagic graph from a previously known distance antimagic graph.

DENSE STABLE RANK AND RUNGE-TYPE APPROXIMATION THEOREMS FOR MAPS

2021 ◽  
pp. 1-29
Author(s):  
ALEXANDER BRUDNYI
Keyword(s):  
Disjoint Union ◽  
A Priori ◽  
Holomorphic Functions ◽  
Stable Rank ◽  
Open Unit ◽  
Uniform Estimates ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Similar Approximation ◽  
Bounded Holomorphic

Abstract Let $H^\infty ({\mathbb {D}}\times {\mathbb {N}})$ be the Banach algebra of bounded holomorphic functions defined on the disjoint union of countably many copies of the open unit disk ${\mathbb {D}}\subset {{\mathbb C}}$ . We show that the dense stable rank of $H^\infty ({\mathbb {D}}\times {\mathbb {N}})$ is $1$ and, using this fact, prove some nonlinear Runge-type approximation theorems for $H^\infty ({\mathbb {D}}\times {\mathbb {N}})$ maps. Then we apply these results to obtain a priori uniform estimates of norms of approximating maps in similar approximation problems for the algebra $H^\infty ({\mathbb {D}})$ .

Vertex Pancyclic Graphs

1999 ◽  
Vol 3 ◽  
pp. 166-170
Author(s):  
Bert Randerath ◽  
Lutz Volkmann ◽  
Ingo Schiermeyer ◽  
Meike Tewes
Keyword(s):  
Pancyclic Graphs

UNDECIDABILITY OF THE THEORIES OF CLASSES OF STRUCTURES

2014 ◽  
Vol 79 (4) ◽  
pp. 1001-1019 ◽  
Author(s):  
ASHER M. KACH ◽  
ANTONIO MONTALBÁN
Keyword(s):  
Direct Product ◽  
Disjoint Union ◽  
Second Order ◽  
Linear Orders ◽  
Second Order Arithmetic ◽  
Order Arithmetic ◽  
Natural Classes ◽  
Product Of Groups

AbstractMany classes of structures have natural functions and relations on them: concatenation of linear orders, direct product of groups, disjoint union of equivalence structures, and so on. Here, we study the (un)decidability of the theory of several natural classes of structures with appropriate functions and relations. For some of these classes of structures, the resulting theory is decidable; for some of these classes of structures, the resulting theory is bi-interpretable with second-order arithmetic.

Bounding Fitting Heights of Two Classes of Character Degree Graphs

2014 ◽  
Vol 21 (02) ◽  
pp. 355-360
Author(s):  
Xianxiu Zhang ◽  
Guangxiang Zhang
Keyword(s):  
Solvable Group ◽  
Disjoint Union ◽  
Character Degree ◽  
Finite Solvable Group ◽  
Total Degree ◽  
Character Degree Graph ◽  
Vertex Set ◽  
Fitting Height ◽  
Degree Graph

In this article, we prove that a finite solvable group with character degree graph containing at least four vertices has Fitting height at most 4 if each derived subgraph of four vertices has total degree not more than 8. We also prove that if the vertex set ρ(G) of the character degree graph Δ(G) of a solvable group G is a disjoint union ρ(G) = π1 ∪ π2, where |πi| ≥ 2 and pi, qi∈ πi for i = 1,2, and no vertex in π1 is adjacent in Δ(G) to any vertex in π2 except for p1p2 and q1q2, then the Fitting height of G is at most 4.

scholarly journals Pancyclic graphs II

1976 ◽  
Vol 20 (1) ◽  
pp. 41-46 ◽  
Author(s):  
J.A Bondy ◽  
A.W Ingleton
Keyword(s):  
Pancyclic Graphs
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