Let D be a digraph with vertex set V(D) .For vertex v V(D), the degree of v, denoted by d(v), is defined as the minimum value if its out-degree  and its in-degree . Now let D be a digraph with minimum degree  and edge-connectivity If  is real number, then the zeroth-order general Randic index is defined by   .  A digraph is maximally edge-connected if . In this paper we present sufficient condi...

Directed s-t connectivity is the problem of detecting whether there is a path from vertex s to vertex t in a directed graph. We present the rst known deterministic sublinear space, polynomial time algorithm for directed s-t connectivity. For n-vertex graphs, our algorithm can use as little as n=2 ( p logn) space while still running in polynomial time.

Connectivity and edge-connectivity of a graph measure the difficulty of breaking the graph apart, but they are very much affected by local aspects like vertex degree. Average connectivity (and analogously, average edge-connectivity) has been introduced to give a more refined measure of the global “amount” of connectivity. In this paper, we prove a relationship between the average connectivity a...

The forgotten topological coindex (also called Lanzhou index) is defined for a simple connected graph G as the sum of the terms du2+dv2 over all non-adjacent vertex pairs uv of G, where du denotes the degree of the vertex u in G. In this paper, we present some inequalit...

the tenacity of a graph g, t(g), is de ned by t(g) = min{[|s|+τ(g-s)]/[ω(g-s)]}, where the minimum is taken over all vertex cutsets s of g. we de ne τ(g - s) to be the number of the vertices in the largest component of the graph g - s, and ω(g - s) be the number of components of g - s.in this paper a lower bound for the tenacity t(g) of a graph with genus γ(g) is obtained using the graph's...

Let G be a connected graph and let c : V (G) → {1, 2, . . . , k} be a coloring of the vertices of G for some positive integer k (where adjacent vertices may be colored the same). The color code of a vertex v of G (with respect to c) is the ordered (k+1)-tuple code(v) = (a0, a1, . . . , ak) where a0 is the color assigned to v and for 1 ≤ i ≤ k, ai is the number of vertices adjacent to v that are...