Regular Connected Bipancyclic Spanning Subgraphs of Torus Networks

2018 ◽  
Vol 28 (04) ◽  
pp. 1850013 ◽  
Author(s):  
Miao Lu ◽  
Shurong Zhang ◽  
Weihua Yang
Keyword(s):  
Dimensional Torus ◽  
Spanning Subgraphs ◽  
Spanning Subgraph ◽  
Strong Property ◽  
Torus Networks

It is well known that an [Formula: see text]-dimensional torus [Formula: see text] is Hamiltonian. Then the torus [Formula: see text] contains a spanning subgraph which is 2-regular and 2-connected. In this paper, we explore a strong property of torus networks. We prove that for any even integer [Formula: see text] with [Formula: see text], the torus [Formula: see text] contains a spanning subgraph which is [Formula: see text]-regular, k-connected and bipancyclic; and if [Formula: see text] is odd, the result holds when some [Formula: see text] is even.

scholarly journals Matching preclusion for n -dimensional torus networks

2017 ◽  
Vol 687 ◽  
pp. 40-47 ◽  
Author(s):  
Xiaomin Hu ◽  
Yingzhi Tian ◽  
Xiaodong Liang ◽  
Jixiang Meng
Keyword(s):  
Dimensional Torus ◽  
Torus Networks

scholarly journals Broadcastings and digit tilings on three-dimensional torus networks

2011 ◽  
Vol 412 (4-5) ◽  
pp. 307-319 ◽  
Author(s):  
Ryotaro Okazaki ◽  
Hirotaka Ono ◽  
Taizo Sadahiro ◽  
Masafumi Yamashita
Keyword(s):  
Three Dimensional ◽  
Dimensional Torus ◽  
Torus Networks

scholarly journals Sparse Highly Connected Spanning Subgraphs in Dense Directed Graphs

2018 ◽  
Vol 28 (3) ◽  
pp. 423-464 ◽  
Author(s):  
DONG YEAP KANG
Keyword(s):  
Upper Bound ◽  
Maximum Degree ◽  
Analogous Result ◽  
Undirected Graph ◽  
Directed Graphs ◽  
Additional Term ◽  
Spanning Subgraphs ◽  
Spanning Subgraph ◽  
Polynomial Time Algorithms ◽  
Bipartite Digraph

Mader proved that every strongly k-connected n-vertex digraph contains a strongly k-connected spanning subgraph with at most 2kn - 2k2 edges, where equality holds for the complete bipartite digraph DKk,n-k. For dense strongly k-connected digraphs, this upper bound can be significantly improved. More precisely, we prove that every strongly k-connected n-vertex digraph D contains a strongly k-connected spanning subgraph with at most kn + 800k(k + Δ(D)) edges, where Δ(D) denotes the maximum degree of the complement of the underlying undirected graph of a digraph D. Here, the additional term 800k(k + Δ(D)) is tight up to multiplicative and additive constants. As a corollary, this implies that every strongly k-connected n-vertex semicomplete digraph contains a strongly k-connected spanning subgraph with at most kn + 800k2 edges, which is essentially optimal since 800k2 cannot be reduced to the number less than k(k - 1)/2.We also prove an analogous result for strongly k-arc-connected directed multigraphs. Both proofs yield polynomial-time algorithms.

scholarly journals Panconnectivity of n-dimensional torus networks with faulty vertices and edges

2013 ◽  
Vol 161 (3) ◽  
pp. 404-423 ◽  
Author(s):  
Jun Yuan ◽  
Aixia Liu ◽  
Hongmei Wu ◽  
Jing Li
Keyword(s):  
Dimensional Torus ◽  
Torus Networks

Conditional fractional matching preclusion of n-dimensional torus networks

2021 ◽  
Vol 293 ◽  
pp. 157-165
Author(s):  
Xiaomin Hu ◽  
Yingzhi Tian ◽  
Jixiang Meng ◽  
Weihua Yang
Keyword(s):  
Dimensional Torus ◽  
Torus Networks

scholarly journals On a Class of Polynomials Associated with the Stars of a Graph and its Application to Node-Disjoint Decompositions of Complete Graphs and Complete Bipartite Graphs into Stars

1979 ◽  
Vol 22 (1) ◽  
pp. 35-46 ◽  
Author(s):  
E. J. Farrell
Keyword(s):  
Connected Graph ◽  
Bipartite Graphs ◽  
Complete Graphs ◽  
Spanning Subgraphs ◽  
Spanning Subgraph ◽  
Complete Bipartite Graphs

AbstractA star is a connected graph in which every node but possibly one has valency 1. Let G be a graph and C a spanning subgraph of G in which every component is a star. With each component α of C let us associate a weight wα. Let Пα wα be the weight associated with the entire subgraph G the star polynomial of G is ΣПα wα where the summation is taken over all spanning subgraphs of G consisting of stars. In this paper an algorithm for finding star polynomials of graphs is given. The star polynomials of various classes of graphs are then found, and some results about node-disjoint decomposition of complete graphs and complete bipartite graphs are deduced.

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