Reliability analysis of godan graphs in terms of generalized 4-connectivity

Let G be a connected graph and S subset of V(G). Denote by kappa(G)(S) the maximum number r of internally disjoint S-trees T-1, T-2, & mldr;, T(r )in G such that V(Ti)boolean AND V(T-j)=S and E(T-i)boolean AND E(T-j)=theta for any integers 1 <= i<j <= r. For an integer k with 2 <= k <=|V(G)|, the generalized k-connectivity of a graph G, denoted by kappa(k)(G), is defined as kappa(k)(G)=min{kappa(G)(S)|S subset of V(G) and |S|=k}. The generalized k-connectivity of a graph is a natural extension of the classical connectivity and plays a key role in measuring the reliability of modern interconnection networks. The godan graph EA(n) is a kind of Cayley graph which possess many desirable properties. In this paper, we study the generalized 4-connectivity of EA(n) and show that kappa(4)(EA(n)) = n - 1, that is, there are n-1 internally disjoint S-trees connecting any four vertices x,y,z and w in EA(n), where n >= 3 and S={x,y,z,w}. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, Al training, and similar technologies.