Edge neighbor connectivity of Cartesian product graph G×K2

2011 ◽  
Vol 217 (12) ◽  
pp. 5508-5511 ◽  
Author(s):  
Xuebin Zhao ◽  
Zhao Zhang ◽  
Qin Ren
Keyword(s):  
Cartesian Product ◽  
Product Graph ◽  
Neighbor Connectivity

scholarly journals Dimensi Metrik Kuat Lokal Graf Hasil Operasi Kali Kartesian

2020 ◽  
Vol 1 (2) ◽  
pp. 64
Author(s):  
Nurma Ariska Sutardji ◽  
Liliek Susilowati ◽  
Utami Dyah Purwati
Keyword(s):  
Graph Theory ◽  
Cartesian Product ◽  
Metric Dimension ◽  
Star Graph ◽  
Product Graph ◽  
Path Graph ◽  
Strong Metric Dimension ◽  
Metric Dimensions ◽  
Development Result ◽  
Corona Product

The strong local metric dimension is the development result of a strong metric dimension study, one of the study topics in graph theory. Some of graphs that have been discovered about strong local metric dimension are path graph, star graph, complete graph, cycle graphs, and the result corona product graph. In the previous study have been built about strong local metric dimensions of corona product graph. The purpose of this research is to determine the strong local metric dimension of cartesian product graph between any connected graph G and H, denoted by dimsl (G x H). In this research, local metric dimension of G x H is influenced by local strong metric dimension of graph G and local strong metric dimension of graph H. Graph G and graph H has at least two order.

Research on the Hereditary Properties of the Cartesian Product Operation of Graphs

2012 ◽  
Vol 241-244 ◽  
pp. 2802-2806
Author(s):  
Hua Dong Wang ◽  
Bin Wang ◽  
Yan Zhong Hu
Keyword(s):  
Euler Characteristic ◽  
Cartesian Product ◽  
Hamilton Cycle ◽  
Hereditary Property ◽  
Constant Property ◽  
Product Graph ◽  
Product Operation ◽  
Graph Operation ◽  
Hereditary Properties

This paper defined the hereditary property (or constant property) concerning graph operation, and discussed various forms of the hereditary property under the circumstance of Cartesian product graph operation. The main conclusions include: The non-planarity and Hamiltonicity of graph are hereditary concerning the Cartesian product, but planarity of graph is not, Euler characteristic and non-hamiltonicity of graph are not hereditary as well. Therefore, when we applied this principle into practice, we testified that Hamilton cycle does exist in hypercube.

On the Hamilton Cycle of the Hypercube

2011 ◽  
Vol 480-481 ◽  
pp. 922-927 ◽  
Author(s):  
Yan Zhong Hu ◽  
Hua Dong Wang
Keyword(s):  
Euler Characteristic ◽  
Interconnection Networks ◽  
Cartesian Product ◽  
Hamilton Cycle ◽  
The Other ◽  
Product Graph ◽  
Product Graphs ◽  
Cartesian Product Graphs ◽  
Isomorphic Graphs ◽  
The Relationship

Hypercube is one of the basic types of interconnection networks. In this paper, we use the concept of the Cartesian product graph to define the hypercube Qn, we study the relationship between the isomorphic graphs and the Cartesian product graphs, and we get the result that there exists a Hamilton cycle in the hypercube Qn. Meanwhile, the other properties of the hypercube Qn, such as Euler characteristic and bipartite characteristic are also introduced.

THE ISOPERIMETRIC NUMBER OF d–DIMENSIONAL k–ARY ARRAYS

1999 ◽  
Vol 10 (03) ◽  
pp. 289-300 ◽  
Author(s):  
M. CEMIL AZIZOĞLU ◽  
ÖMER EĞECIOĞLU
Keyword(s):  
Cartesian Product ◽  
Product Graph ◽  
Path Graph ◽  
Number Formula ◽  
Isoperimetric Number

The d–dimensional k-ary array [Formula: see text] is the d–fold Cartesian product graph of the path graph Pk with k vertices. We show that the (edge) isoperimetric number [Formula: see text] of [Formula: see text] is given by [Formula: see text] and identify the cardinalities and the structure of the isoperimetric sets. For odd k, the cardinalities of isoperimetric sets in [Formula: see text] are [Formula: see text], whereas every isoperimetric set for k even has cardinality [Formula: see text].

scholarly journals Skew Spectra of Oriented Bipartite Graphs

10.37236/3331 ◽  
2013 ◽  
Vol 20 (4) ◽  
Author(s):  
A. Anuradha ◽  
R. Balakrishnan ◽  
Xiaolin Chen ◽  
Xueliang Li ◽  
Huishu Lian ◽  
...  
Keyword(s):  
Bipartite Graph ◽  
Cartesian Product ◽  
Bipartite Graphs ◽  
Affirmative Answer ◽  
Cartesian Products ◽  
Oriented Graphs ◽  
Canonical Orientation ◽  
Product Graph ◽  
Skew Energy ◽  
Cartesian Products Of Graphs

A graph $G$ is said to have a parity-linked orientation $\phi$ if every even cycle $C_{2k}$ in $G^{\phi}$ is evenly (resp. oddly) oriented whenever $k$ is even (resp. odd). In this paper, this concept is used to provide an affirmative answer to the following conjecture of D. Cui and Y. Hou [D. Cui, Y. Hou, On the skew spectra of Cartesian products of graphs, Electronic J. Combin. 20(2):#P19, 2013]: Let $G=G(X,Y)$ be a bipartite graph. Call the $X\rightarrow Y$ orientation of $G,$ the canonical orientation. Let $\phi$ be any orientation of $G$ and let $Sp_S(G^{\phi})$ and $Sp(G)$ denote respectively the skew spectrum of $G^{\phi}$ and the spectrum of $G.$ Then $Sp_S(G^{\phi}) = {\bf{i}} Sp(G)$ if and only if $\phi$ is switching-equivalent to the canonical orientation of $G.$ Using this result, we determine the switch for a special family of oriented hypercubes $Q_d^{\phi},$ $d\geq 1.$ Moreover, we give an orientation of the Cartesian product of a bipartite graph and a graph, and then determine the skew spectrum of the resulting oriented product graph, which generalizes a result of Cui and Hou. Further this can be used to construct new families of oriented graphs with maximum skew energy.

scholarly journals LIGHTS OUT! on graph products over the ring of integers modulo k

2021 ◽  
Vol 37 ◽  
pp. 416-424
Author(s):  
Ryan Munter ◽  
Travis Peters
Keyword(s):  
Cartesian Product ◽  
Simple Graph ◽  
Graph Products ◽  
Ring Of Integers ◽  
Product Graph ◽  
Turn On ◽  
Strong Product ◽  
Product Graphs ◽  
Traditional Game ◽  
Do So

LIGHTS OUT! is a game played on a finite, simple graph. The vertices of the graph are the lights, which may be on or off, and the edges of the graph determine how neighboring vertices turn on or off when a vertex is pressed. Given an initial configuration of vertices that are on, the object of the game is to turn all the lights out. The traditional game is played over $\mathbb{Z}_2$, where the vertices are either lit or unlit, but the game can be generalized to $\mathbb{Z}_k$, where the lights have different colors. Previously, the game was investigated on Cartesian product graphs over $\mathbb{Z}_2$. We extend this work to $\mathbb{Z}_k$ and investigate two other fundamental graph products, the direct (or tensor) product and the strong product. We provide conditions for which the direct product graph and the strong product graph are solvable based on the factor graphs, and we do so using both open and closed neighborhood switching over $\mathbb{Z}_k$.

CARTESIAN PRODUCT ON FUZZY IDEALS OF A TERNARY Γ-SEMIGROUP

2020 ◽  
Vol 9 (3) ◽  
pp. 1189-1195 ◽  
Author(s):  
Y. Bhargavi ◽  
T. Eswarlal ◽  
S. Ragamayi
Keyword(s):  
Cartesian Product
Sign in / Sign up

Export Citation Format

Share Document