Sufficient conditions on the zeroth-order general Randic index for maximally edge-connected digraphs

sufficient conditions on the zeroth-order general randic index for maximally edge-connected digraphs

let $d$ be a digraph with vertex set $v(d)$. for vertex $vin v(d)$, 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 $deltage 1$ and edge-connectivity$lambda$. if $alpha$ is real number, then the zeroth-order general randic index is definedby $sum_{xin v(d)}(d(x))^{alpha}$. a digraph is maximall...

Sufficient conditions for maximally edge-connected and super-edge-connected

Let $G$ be a connected graph with minimum degree $delta$ and edge-connectivity $lambda$. A graph ismaximally edge-connected if $lambda=delta$, and it is super-edge-connected if every minimum edge-cut istrivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree.In this paper, we show that a connected graph or a connected triangle-free graph is maximall...

Sufficient conditions for maximally edge-connected graphs and arc-connected digraphs

A connected graph with edge connectivity λ and minimum degree δ is called maximally edge-connected if λ = δ. A strongly connected digraph with arc connectivity λ and minimum degree δ is called maximally arc-connected if λ = δ. In this paper, some new sufficient conditions are presented for maximally edge-connected graphs and arc-connected digraphs. We only consider finite graphs (digraphs) with...

Maximally edge-connected digraphs

In this paper we present some new sufficient conditions for equality of edge-connectivity and minimum degree of graphs and digraphs as well as of bipartite graphs and digraphs.

Maximal Value of the Zeroth-order Randic Index

Let G(n; m) be a connected graph without loops and multiple edges which has n vertices and m edges. We ÿnd the graphs on which the zeroth-order connectivity index, equal to the sum of degrees of vertices of G(n; m) raised to the power − 1 2 , attains maximum.

Neighborhood conditions for graphs and digraphs to be maximally edge-connected