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Highly Irregular m-Chromatic Graphs
[chapter]

1988
*
Annals of Discrete Mathematics
*

In this paper, we study existence and extremal problems for

doi:10.1016/s0167-5060(08)70765-9
fatcat:ktogduiruzdslm2r4p7psrkdga
*highly**irregular**graphs*with a given maximum degree and focus our attention on*highly**irregular**graphs*that are*m*-*chromatic*for*m*3 2. ... A*graph*is*highly**irregular*if it is connected and the neighbors of each vertex have distinct degrees. ...*m*-*Chromatic**graphs*Corollary 5 has the following generalization kindly communicated to us by Chartrand. Theorem 6. Let G be a*highly**irregular**m*-*chromatic*A-*graph*,*m*2 3. Then A>2m-2. Proof. ...##
###
Highly irregular m-chromatic graphs

1988
*
Discrete Mathematics
*

In this paper, we study existence and extremal problems for

doi:10.1016/0012-365x(88)90188-4
fatcat:3753b6pjfnh2dez5uppwzt53o4
*highly**irregular**graphs*with a given maximum degree and focus our attention on*highly**irregular**graphs*that are*m*-*chromatic*for*m*3 2. ... A*graph*is*highly**irregular*if it is connected and the neighbors of each vertex have distinct degrees. ...*m*-*Chromatic**graphs*Corollary 5 has the following generalization kindly communicated to us by Chartrand. Theorem 6. Let G be a*highly**irregular**m*-*chromatic*A-*graph*,*m*2 3. Then A>2m-2. Proof. ...##
###
Page 1382 of Mathematical Reviews Vol. , Issue 90C
[page]

1990
*
Mathematical Reviews
*

The paper concludes with a few results on

*highly**irregular**m*-*chromatic**graphs*. {For the entire collection see MR 89j:05007a.} Ortrud R. Oellermann (1-WM1I) ... Alan Tucker (1-SUNYS-S) 90c:05079 O05C15 05C05 05C38 Alavi, Yousef (1-WMI); Buckley, Fred (1-CUNY2); Shamula, Marc (1-CUNY2); Ruiz, Sergio (RCH-UCV)*Highly**irregular**m*-*chromatic**graphs*. ...##
###
Author index to volume 145 (1995)

1995
*
Discrete Mathematics
*

Lehel,

doi:10.1016/0012-365x(95)90083-w
fatcat:vssxfxs7c5a4neq6ixqbnr2j24
*Irregular*embeddings of multigraphs with fixed*chromatic*number (Note) (1 3) 295-299 Jendro'l, S. and*M*. ... -*M*. and Y. Liu, On the*chromatic*uniqueness of the*graph*W(n, n -2) + K k (1--3) 95 103 Gravier, S. and A. ... ., Random walks and orthogonal functions associated with*highly*symmetric*graphs*...##
###
Page 774 of Mathematical Reviews Vol. , Issue 99b
[page]

1991
*
Mathematical Reviews
*

Let G be a

*highly**irregular**graph*and A(G) its maximum degree. We show that if A(G) > 2, then 77(G) = A(G) +1. ... Vijayakumar (Cochin) 99b:05068 05C15 Zhang, Xian Di (PRC-EST-AM; Chengdu) Total colorings of*highly**irregular**graphs*of high degree. (Chinese. ...##
###
Page 5292 of Mathematical Reviews Vol. , Issue 93j
[page]

1993
*
Mathematical Reviews
*

of a

*graph*G.” 93j:05063 05C20 Alavi, Yousef (1-WMI); Liu, Jiu Qiang (1-WMI); Wang, Jian Fang (PRC-ASBJ-AM)*Highly**irregular*digraphs. ... In this paper, we investigate some problems concerning the existence of*highly**irregular*digraphs with special properties, with particular focus on*highly**irregular*directed trees as well as their independence ...##
###
Author index to volume 164 (1997)

1997
*
Discrete Mathematics
*

Michael, Degree sequences of

doi:10.1016/s0012-365x(97)84783-8
fatcat:vheqou5bfnhuzbok7wzs3b3kfa
*highly**irregular**graphs*(1-3) 225-236 Majcher, Z. and J. Michael,*Highly**irregular**graphs*with extreme numbers of edges , A. and*M*. ... Volkmann, On cycles through a given vertex in multipar-,*M*. and S. Jendrol, On the d-distance face*chromatic*number of plane*graphs*(1-3) 171-174 Jendrol, S., see*M*. ...##
###
Page 4697 of Mathematical Reviews Vol. , Issue 97H
[page]

1997
*
Mathematical Reviews
*

*irregular*

*graphs*(225-236); Zofia Majcher and Jerzy Michael,

*Highly*

*irregular*

*graphs*with extreme numbers of edges (237-242); Konrad Piwakowski, On Ramsey number R(4, 3,3) and triangle-free edge-

*chromatic*...

*M*. Gutin], Paths and cycles in extended and decomposable digraphs (5-19); Halina Bielak,

*Chromatic*uniqueness in a family of 2-connected

*graphs*(21-28); H. J. ...

##
###
Decomposing Oriented Graphs into Six Locally Irregular Oriented Graphs

2016
*
Graphs and Combinatorics
*

Namely, we prove that every oriented

doi:10.1007/s00373-016-1705-z
fatcat:prgmt2frmzduhbmucfkwih2hgy
*graph*can be decomposed into 6 locally*irregular*oriented*graphs*. ... We say that G is decomposable into k locally*irregular**graphs*if there exists a partition E 1 ∪ E 2 ∪ ... ∪ E k of the edge set E(G) such that each E i induces a locally*irregular**graph*. ... [1] , who defined a*highly**irregular**graph*as a*graph*whose every two adjacent vertices have distinct degrees. ...##
###
Complexity of determining the irregular chromatic index of a graph
[chapter]

2013
*
The Seventh European Conference on Combinatorics, Graph Theory and Applications
*

The

doi:10.1007/978-88-7642-475-5_104
fatcat:3ankb7fbxnhlzgdvojnnzx7jaa
*irregular**chromatic*index χ irr (G) of G is the least number of colours used by a locally*irregular*edge colouring of G (if any). ... A*graph*G is locally*irregular*if adjacent vertices of G have different degrees. ... Locally*irregular**graphs*were first introduced under the name of*highly**irregular**graphs*in a work aiming at defining some possible ways for catching the*irregularity*of*graphs*[2] . ...##
###
New measures of graph irregularity
[article]

2014
*
arXiv
*
pre-print

In this paper, we define and compare four new measures of

arXiv:1305.3570v7
fatcat:ghyms4ysjfh6lh53guejtzbtte
*graph**irregularity*. We use these measures to prove upper bounds for the*chromatic*number and the Colin de Verdiere parameter. ... We also strengthen the concise Turan theorem for*irregular**graphs*and investigate to what extent Turan's theorem can be similarly strengthened for generalized r-partite*graphs*. ... The*graphs*representing some actual networks, such as the World Wide Web, power grids, academic collaborators and neural networks, are*highly**irregular*. ...##
###
Page 5392 of Mathematical Reviews Vol. , Issue 89J
[page]

1989
*
Mathematical Reviews
*

ISBN 0-444-70538-4
Contents: Yousef Alavi, Fred Buckley, Marc Shamula and Sergio Ruiz,

*Highly**irregular**m*-*chromatic**graphs*(pp. 3-13); N. Alon and F. R. K. ... Hedetniemi, The edge sub-*chromatic*number of a*graph*(pp. 95-104); Ehab S. El-Mallah and Charles J. ...##
###
Page 42 of Mathematical Reviews Vol. , Issue 94a
[page]

1994
*
Mathematical Reviews
*

if G is an outerplanar

*graph*. X. D. Zhang and others proved that G € C} if G is a*highly**irregular**graph*, i.e., for any v € V, d(u) 4 d(w) if vv,uw € E. Let G be a simple*graph*. ... if G is a simple*graph*(x(G) and x’(G) are the vertex*chromatic*number and the edge*chromatic*number, respec- tively). ...##
###
Author index to volume

2004
*
Discrete Mathematics
*

Marczyk and

doi:10.1016/s0012-365x(04)00345-0
fatcat:6zribkcwoneppcmbtj3xqfm3qy
*M*. Wo! zniak, A note on pancyclism of*highly*connected*graphs*(1-2) 57-60 Flandrin, E., see M.E.K. Abderrezzak (1-2) 5-13 Fletcher, R.J., C. Koukouvinos and J. ... Kemnitz, The circular*chromatic*index (1-2) 89-93 Ha"uszczak,*M*., see M.x. Borowiecki (1-2) 37-43 Harant, J., On paths and cycles through specified vertices (1-2) 95-98 Harant, J., see F. ... Marczyk and*M*. Wo! zniak, A note on pancyclism of*highly*connected*graphs*, R.J., C. Koukouvinos and J. ...##
###
Structural Fault Detection In Random Macro Textures

1996
*
Zenodo
*

The placement o f the primitives within these is purely random and

doi:10.5281/zenodo.36046
fatcat:cv4mklmt3jd45n6c3ucvojjyxy
*highly**irregular*. ... INTRODUCTION Texture is generally divided into two*m*a i n t ypes: micro and macro textures. ...
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