Reliability evaluation of an interconnection network is of great significance for construction and maintenance of the network. The extra connectivity and essentially edge-connectivity are two important parameters to evaluate network reliability. Let [Formula: see text] be a finite group. The power graph [Formula: see text] of [Formula: see text] is defined as an undirected graph whose vertex set is [Formula: see text] and two distinct vertices [Formula: see text] are adjacent if and only if one is a power of the other. In this paper, we determine the [Formula: see text]-extra connectivity and essentially edge-connectivity of the power graph of a cyclic finite group.
Consider a group [Formula: see text] and construct its power graph, whose vertex set consists of the elements of [Formula: see text]. Two distinct vertices (elements) are adjacent in the graph if and only if one element can be expressed as an integral power of the other. In this article, we improved the bounds of the s...
Priti Prasanna Mondal, Basit A. Mir, Fouzul Atik· Journal of Algebra and its A...· 0 citations
Closed-form expressions for path matrices of length up to four are derived, and a novel indicator of the structural propensity of the graph to form clusters is proposed.
Najaya Al-Hajri, Mohammad Taghi Darvishi, S. Noschese et al.· Mathematics· 0 citations
This work introduces the [Formula: see text]-Steiner-Connectivity Preservation problem where a minimum-cost set of edges are protected such that the underlying graph maintains [Formula: see text]-edge-connectivity between given terminal pairs against edge failures, assuming at most [Formula: see text] unprotected edges...
Felix Hommelsheim, Zhen-Wei Liu, Nicole Megow et al.· SIAM Journal on Discrete Mat...· 0 citations
This work establishes general properties of k -total bondage and finds exact values for certain graph classes including paths, cycles, wheels, complete and complete bipartite graphs.
The results support HON as a simple low-degree construction for structured inter-group communication, whereas higher-radix, adaptive, or more richly connected fabrics remain better suited to less structured traffic and larger bandwidth demand.
Han Ni Soe, Yao Zhang, Zhi-Peng Xu· Parallel Processing Letters· 0 citations
