scholarly journals Equitable Chromatic Number of Complete Multipartite Graphs

2003 ◽  
Vol 15 (2) ◽  
pp. 75-81 ◽  
Author(s):  
Dorothee Blum ◽  
Denise Torrey ◽  
Richard Hammack
Keyword(s):  
Chromatic Number ◽  
Multipartite Graphs ◽  
Complete Multipartite Graphs ◽  
Complete Multipartite ◽  
Equitable Chromatic Number

On the local irregularity vertex coloring of volcano, broom, parachute, double broom and complete multipartite graphs

2021 ◽  
Author(s):  
Arika Indah Kristiana ◽  
Nafidatun Nikmah ◽  
Dafik ◽  
Ridho Alfarisi ◽  
M. Ali Hasan ◽  
...  
Keyword(s):  
Chromatic Number ◽  
Connected Graph ◽  
Vertex Coloring ◽  
Minimum Cardinality ◽  
Label Function ◽  
Multipartite Graphs ◽  
Complete Multipartite Graphs ◽  
Vertex Set ◽  
Complete Multipartite ◽  
Local Irregularity

Let [Formula: see text] be a simple, finite, undirected, and connected graph with vertex set [Formula: see text] and edge set [Formula: see text]. A bijection [Formula: see text] is label function [Formula: see text] if [Formula: see text] and for any two adjacent vertices [Formula: see text] and [Formula: see text], [Formula: see text] where [Formula: see text] and [Formula: see text] is set ofvertices adjacent to [Formula: see text]. [Formula: see text] is called local irregularity vertex coloring. The minimum cardinality of local irregularity vertex coloring of [Formula: see text] is called chromatic number local irregular denoted by [Formula: see text]. In this paper, we verify the exact values of volcano, broom, parachute, double broom and complete multipartite graphs.

scholarly journals On DRC-covering of K(n) t λ by cycles

2009 ◽  
Vol 6 (2) ◽  
pp. 229-237 ◽  
Author(s):  
Zhihe Liang
Keyword(s):  
Lower Bound ◽  
Wdm Networks ◽  
Optimal Solutions ◽  
Multipartite Graphs ◽  
Complete Multipartite Graphs ◽  
Number Of Cycles ◽  
Complete Multipartite

This paper considers the cycle covering of complete multipartite graphs motivated by the design of survivable WDM networks, where the requests are routed on sub-networks which are protected independently from each other. The problem can be stated as follows: for a given graph G, find a cycle covering of the edge set of K (n) t ? , where V( Kt (n))=V(G), such that each cycle in the covering satisfies the disjoint routing constraint (DRC). Here we consider the case where G=Ctn, a ring of size tn and we want to minimize the number of cycles ? (nt, ?) in the covering. For the problem, we give the lower bound of ? (nt, ?), and obtain the optimal solutions when n is even or n is odd and both ? and t are even.

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