Connectivity of path 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...

Eccentric Connectivity Index of Some Dendrimer Graphs

The eccentricity connectivity index of a molecular graph G is defined as (G) = aV(G) deg(a)ε(a), where ε(a) is defined as the length of a maximal path connecting a to other vertices of G and deg(a) is degree of vertex a. Here, we compute this topological index for some infinite classes of dendrimer graphs.

Eccentric Connectivity Index: Extremal Graphs and Values

Eccentric connectivity index has been found to have a low degeneracy and hence a significant potential of predicting biological activity of certain classes of chemical compounds. We present here explicit formulas for eccentric connectivity index of various families of graphs. We also show that the eccentric connectivity index grows at most polynomially with the number of vertices and determine ...