Multilevelk-way Partitioning Scheme for Irregular Graphs

1998 ◽  
Vol 48 (1) ◽  
pp. 96-129 ◽  
Author(s):  
George Karypis ◽  
Vipin Kumar
Keyword(s):  
Irregular Graphs

scholarly journals Non-Neighbour Irregular Graphs

2016 ◽  
Vol 15 ◽  
pp. 1-7
Author(s):  
B. Basavanagoud ◽  
H.S. Ramane ◽  
Veena R. Desai
Keyword(s):  
Irregular Graphs

A graph G is said to be non-neighbour irregular graph if no two nonadjacent vertices of G have same degree. This paper suggests the methods of construction of non-neighbour irregular graphs. This paper also includes a few properties possessed by these non-neighbour irregular graphs.

scholarly journals Can Colour-Blind Distinguish Colour Palettes?

10.37236/2319 ◽  
2013 ◽  
Vol 20 (3) ◽  
Author(s):  
Rafał Kalinowski ◽  
Monika Pilśniak ◽  
Jakub Przybyło ◽  
Mariusz Woźniak
Keyword(s):  
Large Degree ◽  
Bipartite Graphs ◽  
Complete Graphs ◽  
Regular Graphs ◽  
Lovász Local Lemma ◽  
Local Lemma ◽  
Comprehensive Information ◽  
Lovasz Local Lemma ◽  
Delta G ◽  
Irregular Graphs

Let $c:E(G)\rightarrow [k]$ be  a colouring, not necessarily proper, of edges of a graph $G$. For a vertex $v\in V$, let $\overline{c}(v)=(a_1,\ldots,a_k)$, where $ a_i =|\{u:uv\in E(G),\;c(uv)=i\}|$, for $i\in [k].$ If we re-order the sequence $\overline{c}(v)$ non-decreasingly, we obtain a sequence $c^*(v)=(d_1,\ldots,d_k)$, called a palette of a vertex $v$. This can be viewed as the most comprehensive information about colours incident with $v$ which can be delivered by a person who is unable to name colours but distinguishes one from another. The smallest $k$ such that $c^*$ is a proper colouring of vertices of $G$ is called the colour-blind index of a graph $G$, and is denoted by dal$(G)$. We conjecture that there is a constant $K$ such that dal$(G)\leq K$ for every graph $G$ for which the parameter is well defined. As our main result we prove that $K\leq 6$ for regular graphs of sufficiently large degree, and for irregular graphs with $\delta (G)$ and $\Delta(G)$ satisfying certain conditions. The proofs are based on the Lopsided Lovász Local Lemma. We also show that $K=3$ for all regular bipartite graphs, and for complete graphs of order $n\geq 8$.

scholarly journals The spectral radius of irregular graphs

2009 ◽  
Vol 431 (1-2) ◽  
pp. 189-196 ◽  
Author(s):  
Lingsheng Shi
Keyword(s):  
Spectral Radius ◽  
Irregular Graphs

Classifying Graphs

2017 ◽  
Author(s):  
Arthur Benjamin ◽  
Gary Chartrand ◽  
Ping Zhang
Keyword(s):  
Graph Theory ◽  
Rational Number ◽  
Regular Graphs ◽  
Weighted Graphs ◽  
Reconstruction Problem ◽  
Regular Polyhedra ◽  
Four Color Theorem ◽  
Stanislaw Ulam ◽  
Irregular Graphs ◽  
Isomorphic Graphs

This chapter considers the richness of mathematics and mathematicians' responses to it, with a particular focus on various types of graphs. It begins with a discussion of theorems from many areas of mathematics that have been judged among the most beautiful, including the Euler Polyhedron Formula; the number of primes is infinite; there are five regular polyhedra; there is no rational number whose square is 2; and the Four Color Theorem. The chapter proceeds by describing regular graphs, irregular graphs, irregular multigraphs and weighted graphs, subgraphs, and isomorphic graphs. It also analyzes the degrees of the vertices of a graph, along with concepts and ideas concerning the structure of graphs. Finally, it revisits a rather mysterious problem in graph theory, introduced by Stanislaw Ulam and Paul J. Kelly, that no one has been able to solve: the Reconstruction Problem.

F-Irregular Graphs

2021 ◽  
pp. 27-32
Author(s):  
Akbar Ali ◽  
Gary Chartrand ◽  
Ping Zhang
Keyword(s):  
Irregular Graphs

scholarly journals Constructing new families of transmission irregular graphs

2021 ◽  
Vol 289 ◽  
pp. 383-391
Author(s):  
Kexiang Xu ◽  
Sandi Klavžar
Keyword(s):  
Irregular Graphs

On the maximum size of stepwise irregular graphs

2021 ◽  
Vol 392 ◽  
pp. 125683
Author(s):  
Lkhagva Buyantogtokh ◽  
Enkhbayar Azjargal ◽  
Batmend Horoldagva ◽  
Shiikhar Dorjsembe ◽  
Damchaa Adiyanyam
Keyword(s):  
Maximum Size ◽  
Irregular Graphs

Stepwise transmission irregular graphs

2020 ◽  
Vol 371 ◽  
pp. 124949
Author(s):  
Andrey A. Dobrynin ◽  
Reza Sharafdini
Keyword(s):  
Irregular Graphs
Sign in / Sign up

Export Citation Format

Share Document