scholarly journals Some new results on the join graph of given groups

Mathematica ◽  
2018 ◽  
Vol 60 (83) (1) ◽  
pp. 3-11
Author(s):  
Arefeh Asrari ◽  
◽  
Behnaz Tolue ◽  
Keyword(s):  
Join Graph

scholarly journals Minimal join graph set synthesis self-managing cliques algorithm

2014 ◽  
Vol 1 (12) ◽  
pp. 119
Author(s):  
Andrey Alexandrovich Filchenkov
Keyword(s):  
Join Graph ◽  
Graph Set

scholarly journals Computing the Atom Graph of a Graph and the Union Join Graph of a Hypergraph

Algorithms ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 347
Author(s):  
Anne Berry ◽  
Geneviève Simonet
Keyword(s):  
Real Number ◽  
Time Complexity ◽  
Matrix Multiplication ◽  
Efficient Algorithms ◽  
Join Graph ◽  
Current Value ◽  
Minimal Separator

The atom graph of a graph is a graph whose vertices are the atoms obtained by clique minimal separator decomposition of this graph, and whose edges are the edges of all possible atom trees of this graph. We provide two efficient algorithms for computing this atom graph, with a complexity in O(min(nωlogn,nm,n(n+m¯)) time, where n is the number of vertices of G, m is the number of its edges, m¯ is the number of edges of the complement of G, and ω, also denoted by α in the literature, is a real number, such that O(nω) is the best known time complexity for matrix multiplication, whose current value is 2,3728596. This time complexity is no more than the time complexity of computing the atoms in the general case. We extend our results to α-acyclic hypergraphs, which are hypergraphs having at least one join tree, a join tree of an hypergraph being defined by its hyperedges in the same way as an atom tree of a graph is defined by its atoms. We introduce the notion of union join graph, which is the union of all possible join trees; we apply our algorithms for atom graphs to efficiently compute union join graphs.

The Smarandachely Adjacent Vertex Distinguishing E-Total Coloring of some Join Graphs

2013 ◽  
Vol 475-476 ◽  
pp. 379-382
Author(s):  
Mu Chun Li ◽  
Shuang Li Wang ◽  
Li Li Wang
Keyword(s):  
Chromatic Number ◽  
Total Coloring ◽  
Adjacent Vertex ◽  
Analysis Method ◽  
Total Chromatic Number ◽  
Join Graph ◽  
Total Coloring Conjecture

Using the analysis method and the function of constructing the Smarandachely adjacent vertex distinguishing E-total coloring function, the Smarandachely adjacent vertex distinguishing E-total coloring of join graphs are mainly discussed, and the Smarandachely adjacent vertex distinguishing E-total chromatic number of join graph are obtained. The Smarandachely adjacent vertex distinguishing E-total coloring conjecture is further validated.

Some Holey Designs and Incomplete Designs for the Join Graph of and with a Pendent Edge

2013 ◽  
Vol 347-350 ◽  
pp. 2885-2888
Author(s):  
Xiao Shan Liu ◽  
Qi Wang
Keyword(s):  
Join Graph ◽  
Incomplete Designs ◽  
Vertex Set

A-design of is a pair , where is the vertex set of and is a collection of subgraphs of , such that each block is isomorphic to and any two distinct vertices in are joined in exact (at most, at least) blocks of . In this paper, we will discuss some holey designs and incomplete designs for the join graph of and with a pendent edge for .

scholarly journals Join graph edges in context of algebraic Bayesian network minimal join graph cliques comparative analysis

2014 ◽  
Vol 3 (14) ◽  
pp. 132
Author(s):  
Andrey Alexandrovich Filchenkov ◽  
Alexander Lvovich Tulupyev ◽  
Vladimirovich Alexander Sirotkin
Keyword(s):  
Comparative Analysis ◽  
Bayesian Network ◽  
Join Graph

scholarly journals <i>L</i>(2,1)-Labeling Number of the Product and the Join Graph on Two Fans

2013 ◽  
Vol 04 (07) ◽  
pp. 1094-1096
Author(s):  
Sumei Zhang ◽  
Qiaoling Ma
Keyword(s):  
Join Graph

scholarly journals The Local Antimagic Chromatic Numbers of Some Join Graphs

2021 ◽  
Vol 26 (4) ◽  
pp. 80
Author(s):  
Xue Yang ◽  
Hong Bian ◽  
Haizheng Yu ◽  
Dandan Liu
Keyword(s):  
Partial Solution ◽  
Vertex Coloring ◽  
Chromatic Numbers ◽  
Infinite Class ◽  
Antimagic Labeling ◽  
Join Graph ◽  
Complement Graph ◽  
Minimum Number ◽  
Vertex Label ◽  
Proper Vertex

Let G=(V(G),E(G)) be a connected graph with n vertices and m edges. A bijection f:E(G)→{1,2,⋯,m} is an edge labeling of G. For any vertex x of G, we define ω(x)=∑e∈E(x)f(e) as the vertex label or weight of x, where E(x) is the set of edges incident to x, and f is called a local antimagic labeling of G, if ω(u)≠ω(v) for any two adjacent vertices u,v∈V(G). It is clear that any local antimagic labelling of G induces a proper vertex coloring of G by assigning the vertex label ω(x) to any vertex x of G. The local antimagic chromatic number of G, denoted by χla(G), is the minimum number of different vertex labels taken over all colorings induced by local antimagic labelings of G. In this paper, we present explicit local antimagic chromatic numbers of Fn∨K2¯ and Fn−v, where Fn is the friendship graph with n triangles and v is any vertex of Fn. Moreover, we explicitly construct an infinite class of connected graphs G such that χla(G)=χla(G∨K2¯), where G∨K2¯ is the join graph of G and the complement graph of complete graph K2. This fact leads to a counterexample to a theorem of Arumugam et al. in 2017, and our result also provides a partial solution to Problem 3.19 in Lau et al. in 2021.

The Wireless Sensor Networks Based on Adjacent Strong Edge Chromatic Number

2014 ◽  
Vol 981 ◽  
pp. 474-477
Author(s):  
Zong Jian Sun ◽  
Jing Chen
Keyword(s):  
Wireless Sensor Networks ◽  
Wireless Sensor Network ◽  
Sensor Network ◽  
Chromatic Number ◽  
Basic Principle ◽  
Optimization Design ◽  
Edge Coloring ◽  
Wireless Sensor ◽  
Join Graph ◽  
Adjacent Strong Edge Coloring

The adjacent strong edge chromatic number of graphs can be applied to the optimization design of wireless sensor network to make the network design more reasonable. An algorithm,based on the basic principle of page sorting technology, is designed to search for the adjacent strong edge coloring of certain join graphs. Therefore, the adjacent strong edge chromatic number of a join graph is obtained, and it can avoid the repetition of wireless sensor network.

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