scholarly journals Line graphs of complete multipartite graphs have small cycle double covers

2002 ◽  
Vol 257 (1) ◽  
pp. 39-61 ◽  
Author(s):  
J.M. Fish ◽  
R. Klimmek ◽  
K. Seyffarth
Keyword(s):  
Line Graphs ◽  
Multipartite Graphs ◽  
Complete Multipartite Graphs ◽  
Small Cycle ◽  
Double Covers ◽  
Complete Multipartite

scholarly journals Line Graphs and Middle Graphs that are Divisor Graphs

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Line Graphs ◽  
Complete Graphs ◽  
Permutation Graphs ◽  
Multipartite Graphs ◽  
Complete Multipartite Graphs ◽  
Complete Multipartite ◽  
Cycle Permutation

In this paper it is determined when the line graphs and the middle graphs of some classes of graphs are divisor graphs. Complete characterizations for cycles, trees, complete graphs and complete multipartite graphs whose line graphs (middle graphs) are divisor graphs are obtained. It is also shown that the line graphs and the middle graphs of the cycle permutation graphs are never divisor graphs.

scholarly journals Circular Intensely Orthogonal Double Cover Design of Balanced Complete Multipartite Graphs

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1743 ◽  
Author(s):  
M. Higazy ◽  
A. El-Mesady ◽  
Emad E. Mahmoud ◽  
Monagi H. Alkinani
Keyword(s):  
Double Cover ◽  
Direct Application ◽  
Spanning Subgraphs ◽  
Multipartite Graphs ◽  
Complete Multipartite Graphs ◽  
Double Covers ◽  
Cover Design ◽  
Complete Multipartite ◽  
Orthogonal Double Cover

In this paper, we generalize the orthogonal double covers (ODC) of Kn,n as follows. The circular intensely orthogonal double cover design (CIODCD) of X=Kn,n,…,n︸m is defined as a collection T={G00,G10,…,G(n−1)0}∪{G01,G11,…,G(n−1)1} of isomorphic spanning subgraphs of X such that every edge of X appears twice in the collection T,E(Gi0)∩E(Gj0)=E(Gi1)∩E(Gj1)=0,i≠jand E(Gi0)∩E(Gj1)=λ=m2,i,j∈ℤn. We define the half starters and the symmetric starters matrices as constructing methods for the CIODCD of X. Then, we introduce some results as a direct application to the construction of CIODCD of X by the symmetric starters matrices.

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.

Sign in / Sign up

Export Citation Format

Share Document