scholarly journals Nearly Gorenstein Rings Arising from Finite Graphs

2021 ◽  
Vol 28 (3) ◽  
Author(s):  
Takayuki Hibi ◽  
Dumitru I. Stamate
Keyword(s):  
Perfect Graphs ◽  
Stable Set ◽  
Gorenstein Rings ◽  
Finite Graphs ◽  
Multipartite Graphs ◽  
Complete Multipartite Graphs ◽  
Complete Multipartite

The classification of complete multipartite graphs whose edge rings are nearly Gorenstein as well as that of finite perfect graphs whose stable set rings are nearly Gorenstein is achieved.

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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