The generalized k-connectivity κk(G) of a graph G was introduced by Chartrand et al. in 1984. It is natural to introduce the concept of generalized k-edge-connectivity, λk(G). For general k, the generalized k-edgeconnectivity of a complete graph is obtained. For k ≥ 3, tight upper and lower bounds of κk(G) and λk(G) are given for a connected graph G of order n, namely, 1 ≤ κk(G) ≤ n− k2 and 1 ≤...

Molecular descriptors are a basic tool in the spectral graph, molecular chemistry, and various other fields of mathematics chemistry. Kulli–Basava K mathvariant="fraktur">B indices were initiated for chemical applicatio...

The generalized theta graph s 1 ;:::;s k consists of a pair of endvertices joined by k internally disjoint paths of lengths s 1 ; : : :; s k 1. We prove that the roots of the chromatic polynomial ((s 1 ;:::;s k ; z) of a k-ary generalized theta graph all lie in the disc jz ? 1j 1 + o(1)] k= logk, uniformly in the path lengths s i. Moreover, we prove that 2;:::;2 ' K 2;k indeed has a chromatic r...

The main objective of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. We establish some results related to the newly defined fractional operator such as Mellin transform and relations to khypergeometric and k-Appell’s functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and Wright hypergeometric functions.

The close form of some integrals involving recently developed generalized k-Struve functions is obtained. The outcome of these integrations is expressed in terms of generalized Wright functions. Several special cases are deduced which lead to some known results.

We present the latest developments on the number of (≤ k)-sets and halving lines for (generalized) configurations of points; as well as the rectilinear and pseudolinear crossing numbers of Kn. In particular, we define perfect generalized configurations on n points as those whose number of (≤ k)-sets is exactly 3¡k+1 2 ¢ for all k ≤ n/3. We conjecture that for each n there is a perfect configura...

An instance of the k-generalized connectivity problem consists of an undirected graph G = (V, E), whose edges are associated with non-negative costs, and a collectionD = {(S1, T1), . . . , (Sd, Td)} of distinct demands, each of which comprises a pair of disjoint vertex sets. We say that a subgraph H ⊆ G connects a demand (Si, Ti) when it contains a path with one endpoint in Si and the other in ...

Md. Abul Kashem 1, Xiao Zhou 2 and Takao Nishizeki 1 1 Graduate School of Information Sciences z Education Center for Information Processing Tohoku University, Senda2 980-77, 3apan. E~aail : [email protected], [email protected] [email protected] Abst ract . A c-vertex-ranking of a graph G for a positive integer c is a labeling of the vertices of G with integers such ...