Abstract It is well-known that every Eulerian orientation of an 2 k -edge-connected undirected graph -arc-connected. A long-standing goal in the area has been to obtain analogous results for vertex-connectivity. Levit, Chandran and Cheriyan recently proved Levit et al. (2018) a hypercube dimension -vertex-connected. Here we provide elementary proof this result. We also show other families -regu...

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.

The atom bond connectivity index of a graph is a new topological index was defined by E. Estrada as ABC(G)  uvE (dG(u) dG(v) 2) / dG(u)dG(v) , where G d ( u ) denotes degree of vertex u. In this paper we present some bounds of this new topological index.

Vertex-connectivity and edge-connectivity represent the extent to which a graph is connected. Study of these key properties of graphs plays an important role in varieties of computer science applications. Recent years have witnessed a number of linear time 3-edge-connectivity algorithms with increasing simplicity. In contrast, the state-of-the-art algorithm for 3-vertex-connectivity due to Hopc...

Let $Gamma_{n,kappa}$ be the class of all graphs with $ngeq3$ vertices and $kappageq2$ vertex connectivity. Denote by $Upsilon_{n,beta}$ the family of all connected graphs with $ngeq4$ vertices and matching number $beta$ where $2leqbetaleqlfloorfrac{n}{2}rfloor$. In the classes of graphs $Gamma_{n,kappa}$ and $Upsilon_{n,beta}$, the elements having maximum augmented Zagreb index are determined.

For a connected graph, a minimum vertex separator is a minimum set of vertices whose removal creates at least two connected components. The vertex connectivity of the graph refers to the size of the minimum vertex separator and a graph is k-vertex connected if its vertex connectivity is k, k ≥ 1. Given a k-vertex connected graph G, the combinatorial problem vertex connectivity augmentation asks...

The class of star graphs is a popular topology for interconnection networks. However it has certain deficiencies. A class of generalization of star graphs called (n, k)-star graphs was introduced in [12] to address these issues. In this paper we will consider the vertex-connectivity of the directed (n, k)-star graph, −−→ Sn,k, given in [8], and show that it is maximally connected.

the atom bond connectivity index of a graph is a new topological index was defined by e.estrada as abc(g)  uve (dg(u) dg(v) 2) / dg(u)dg(v) , where g d ( u ) denotes degreeof vertex u. in this paper we present some bounds of this new topological index.