The universal cyclic edge-connectivity of a graph G is the least k such that there exists set edges whose removal disconnects into components where every component contains cycle. We show for graphs minimum degree at 3 and girth g 4, bounded above by \((\Delta -2)g\) \(\Delta \) maximum degree. then prove if second eigenvalue adjacency matrix d-regular \(g\ge 4\) sufficiently small, \((d-2)g\),...

We present a specialised constraint for enforcing graph connectivity. It is assumed that we have a square symmetrical array A of 0/1 constrained integer variables representing potential undirected edges in a simple graph, such that variable A[u, v] corresponds to the undirected edge (u, v). A search process is then at liberty to select and reject edges. The connectivity constraint ensures that ...

We prove a decomposition result for locally finite graphs which can be used to extend results on edge-connectivity from finite to infinite graphs. It implies that every 4k-edge-connected graph G contains an immersion of some finite 2k-edge-connected Eulerian graph containing any prescribed vertex set (while planar graphs show that G need not contain a subdivision of a simple finite graph of lar...

A permutation graph G of a graph G (or generalized prism) is obtained by taking two disjoint copies of G and adding an arbitrary matching between the copies. For the parameters diameter, radius, average distance, connectivity and edge-connectivity, we compare the values of the parameter for G and G. In particular we show that if G has no isolates and is not 2Kk for k odd, then there exists a pe...