Construction of Antimagic Labeling for the Cartesian Product of Regular Graphs

2011 ◽  
Vol 5 (1) ◽  
pp. 81-87 ◽  
Author(s):  
Oudone Phanalasy ◽  
Mirka Miller ◽  
Costas S. Iliopoulos ◽  
Solon P. Pissis ◽  
Elaheh Vaezpour
Keyword(s):  
Cartesian Product ◽  
Regular Graphs ◽  
Antimagic Labeling

scholarly journals Long-Scale Ollivier Ricci Curvature of Graphs

2019 ◽  
Vol 7 (1) ◽  
pp. 22-44
Author(s):  
D. Cushing ◽  
S. Kamtue
Keyword(s):  
Ricci Curvature ◽  
Piecewise Linear ◽  
Cartesian Product ◽  
Regular Graphs ◽  
Short Scale

Abstract We study the long-scale Ollivier Ricci curvature of graphs as a function of the chosen idleness. Similarly to the previous work on the short-scale case, we show that this idleness function is concave and piecewise linear with at most 3 linear parts. We provide bounds on the length of the first and last linear pieces. We also study the long-scale curvature for the Cartesian product of two regular graphs.

scholarly journals Antimagic Labeling of Regular Graphs

2015 ◽  
Vol 82 (4) ◽  
pp. 339-349 ◽  
Author(s):  
Feihuang Chang ◽  
Yu-Chang Liang ◽  
Zhishi Pan ◽  
Xuding Zhu
Keyword(s):  
Regular Graphs ◽  
Antimagic Labeling

scholarly journals Bakry–Émery Curvature Functions on Graphs

2019 ◽  
Vol 72 (1) ◽  
pp. 89-143 ◽  
Author(s):  
David Cushing ◽  
Shiping Liu ◽  
Norbert Peyerimhoff
Keyword(s):  
Lower Bound ◽  
Spectral Properties ◽  
Cayley Graphs ◽  
Cartesian Product ◽  
Upper And Lower Bounds ◽  
Curvature Function ◽  
Regular Graphs ◽  
Weighted Graphs ◽  
Local Structures ◽  
Local Properties

AbstractWe study local properties of the Bakry–Émery curvature function ${\mathcal{K}}_{G,x}:(0,\infty ]\rightarrow \mathbb{R}$ at a vertex $x$ of a graph $G$ systematically. Here ${\mathcal{K}}_{G,x}({\mathcal{N}})$ is defined as the optimal curvature lower bound ${\mathcal{K}}$ in the Bakry–Émery curvature-dimension inequality $CD({\mathcal{K}},{\mathcal{N}})$ that $x$ satisfies. We provide upper and lower bounds for the curvature functions, introduce fundamental concepts like curvature sharpness and $S^{1}$-out regularity, and relate the curvature functions of $G$ with various spectral properties of (weighted) graphs constructed from local structures of $G$. We prove that the curvature functions of the Cartesian product of two graphs $G_{1},G_{2}$ are equal to an abstract product of curvature functions of $G_{1},G_{2}$. We explore the curvature functions of Cayley graphs and many particular (families of) examples. We present various conjectures and construct an infinite increasing family of 6-regular graphs which satisfy $CD(0,\infty )$ but are not Cayley graphs.

scholarly journals Cartesian Products of Some Regular Graphs Admitting Antimagic Labeling for Arbitrary Sets of Real Numbers

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Yi-Wu Chang ◽  
Shan-Pang Liu
Keyword(s):  
Complete Graphs ◽  
Regular Graphs ◽  
Real Numbers ◽  
Cartesian Products ◽  
Antimagic Labeling ◽  
Edge Labeling

An edge labeling of graph G with labels in A is an injection from E G to A , where E G is the edge set of G , and A is a subset of ℝ . A graph G is called ℝ -antimagic if for each subset A of ℝ with A = E G , there is an edge labeling with labels in A such that the sums of the labels assigned to edges incident to distinct vertices are different. The main result of this paper is that the Cartesian products of complete graphs (except K 1 ) and cycles are ℝ -antimagic.

On a Relationship between Completely Separating Systems and Antimagic Labeling of Regular Graphs

2011 ◽  
pp. 238-241 ◽  
Author(s):  
Oudone Phanalasy ◽  
Mirka Miller ◽  
Leanne Rylands ◽  
Paulette Lieby
Keyword(s):  
Regular Graphs ◽  
Antimagic Labeling

Some Methods for constructing infinite Families of Quasi-Strongly regular Graphs

2020 ◽  
Vol 13 ◽  
Author(s):  
Gholam Hassan Shirdel ◽  
Adel Asgari
Keyword(s):  
Cartesian Product ◽  
Necessary Condition ◽  
Strongly Regular Graphs ◽  
Regular Graphs ◽  
Strongly Regular

: In this article, we examined some method of constructing infinite families of semi-strongly regular graphs, Also we obtained a necessary condition for the composition of several graphs to be semi-strongly regular graphs, and using it, we have constructed some infinite families of semi-strongly regular graphs, Also by using the Cartesian product of two graphs, we have constructed some infinite families of semi-strongly regular graphs.

scholarly journals On antimagic labeling of regular graphs with particular factors

2013 ◽  
Vol 23 ◽  
pp. 76-82 ◽  
Author(s):  
Tao-Ming Wang ◽  
Guang-Hui Zhang
Keyword(s):  
Regular Graphs ◽  
Antimagic Labeling

Super edge- and point-connectivities of the Cartesian product of regular graphs

Networks ◽  
2002 ◽  
Vol 40 (2) ◽  
pp. 91-96 ◽  
Author(s):  
Bih-Sheue Shieh
Keyword(s):  
Cartesian Product ◽  
Regular Graphs

scholarly journals The Number of Spanning Trees of the Cartesian Product of Regular Graphs

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Mei-Hui Wu ◽  
Long-Yeu Chung
Keyword(s):  
Simple Formula ◽  
Spanning Trees ◽  
Cartesian Product ◽  
Regular Graphs ◽  
Electrical Circuits ◽  
Important Measure ◽  
Computational Perspective ◽  
Regular Networks ◽  
Number Of Spanning Trees

The number of spanning trees in graphs or in networks is an important issue. The evaluation of this number not only is interesting from a mathematical (computational) perspective but also is an important measure of reliability of a network or designing electrical circuits. In this paper, a simple formula for the number of spanning trees of the Cartesian product of two regular graphs is investigated. Using this formula, the number of spanning trees of the four well-known regular networks can be simply taken into evaluation.

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