Path-connectivity in graphs

Connectivity of path graphs

We prove a necessary and sufficient condition under which a connected graph has a connected P3-path graph. Moreover, an analogous condition for connectivity of the Pk-path graph of a connected graph which does not contain a cycle of length smaller than k+1 is derived.

Long path connectivity of regular graphs

Edge-connectivity and super edge-connectivity of P2-path graphs

For a graph G, the P2-path graph, P2(G), has for vertices the set of all paths of length 2 in G. Two vertices are connected when their union is a path or a cycle of length 3. We present lower bounds on the edge-connectivity, (P2(G)) of a connected graph G and give conditions for maximum connectivity. A maximally edge-connected graph is superif each minimum edge cut is trivial, and it is optimum...

Memory Paging for Connectivity and Path Problems in Graphs

We extend the Paging Problem to the case in which the items that are stored in the cache memory represent information about a graph. We propose on-line algorithms for two different connectivity problems in this context, for particular classes of graphs and under different cost assumptions. In the Path-paging problem we assume that the cache contains edges of the graph and queries to be answered...

Incidence cuts and connectivity in fuzzy incidence graphs

Fuzzy incidence graphs can be used as models for nondeterministic interconnection networks having extra node-edgerelationships. For example, ramps in a highway system may be modeled as a fuzzy incidence graph so that unexpectedflow between cities and highways can be effectively studied and controlled. Like node and edge connectivity in graphs,node connectivity and arc connectivity in fuzzy inci...