**Volume 21** ▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4

**On the inequalities for beta function**

*Original research paper. Pages 1–7*

Barkat Ali Bhayo and József Sándor

Full paper (PDF, 152 Kb) | Abstract

**Some infinite series involving arithmetic functions**

*Original research paper. Pages 8–14*

Ramesh Kumar Muthumalai

Full paper (PDF, 172 Kb) | Abstract

*k*) and (2|

*k*). Using these identities, some Dirichlet series are expressed in terms of Hurwitz zeta function.

**On some Pascal’s like triangles. Part 9**

*Original research paper. Pages 15–22*

Krassimir T. Atanassov

Full paper (PDF, 131 Kb) | Abstract

**On some Pascal’s like triangles. Part 10**

*Original research paper. Pages 23–34*

Krassimir T. Atanassov

Full paper (PDF, 150 Kb) | Abstract

**The Golden Ratio family and the Binet equation**

*Original research paper. Pages 35–42*

A. G. Shannon and J. V. Leyendekkers

Full paper (PDF, 101 Kb) | Abstract

*F*(

_{n}*a*)}, where the sequence of ordinary Fibonacci numbers can be expressed as {

*F*(5)} in this notation. A generalized Binet equation can predict all the elements of the Golden Ratio family of sequences. Identities analogous to those of the ordinary Fibonacci sequence are developed as extensions of work by Filipponi, Monzingo and Whitford in

_{n}*The Fibonacci Quarterly*, by Horadam and Subba Rao in the

*Bulletin of the Calcutta Mathematical Society*, within the framework of Sloane’s

*Online Encyclopedia of Interger Sequences*.

**More new properties of modified Jacobsthal and Jacobsthal–Lucas numbers**

*Original research paper. Pages 43–54*

Julius Fergy T. Rabago

Full paper (PDF, 192 Kb) | Abstract

and Jacobsthal–Lucas numbers (Shang, 2012).

**On right circulant matrices with general number sequence**

*Original research paper. Pages 55–58*

Aldous Cesar F. Bueno

Full paper (PDF, 140 Kb) | Abstract

**On directed pathos line cut vertex digraph of an arborescence**

*Original research paper. Pages 59–69*

Nagesh H. M. and R. Chandrasekhar

Full paper (PDF, 630 Kb) | Abstract

*n*(

*D*) of a digraph

*D*and the directed pathos line cut vertex digraph

*DPn*(

*T*) of an arborescence

*T*. Planarity, outer planarity, maximal outer planarity, minimally non-outer planarity, and crossing number one properties of

*DPn*(

*T*) are discussed. Also, the problem of reconstructing an arborescence from its directed pathos line cut vertex digraph is presented.

**On Π _{k}–connectivity of some product graphs**

*Original research paper. Pages 70–79*

B. Chaluvaraju, Medha Itagi Huilgol, Manjunath N. and Syed Asif Ulla S.

Full paper (PDF, 278 Kb) | Abstract

*k*be a positive integer. A graph

*G*= (

*V*,

*E*) is said to be Π

*k*-connected if for any given subset

*S*of

*V*(

*G*) with |

*S*| =

*k*, the subgraph induced by

*S*is connected. In this paper, we consider Π

_{k}–connected graphs under different graph valued functions. Π

_{k}–connectivity of Cartesian product, normal product, join and corona of two graphs have been obtained in this paper.

**Embedding index in some classes of graphs**

*Original research paper. Pages 80–88*

M. Kamal Kumar and R. Murali

Full paper (PDF, 144 Kb) | Abstract

*S*of the vertex set of a graph

*G*is called a dominating set of

*G*if each vertex of

*G*is either in

*S*or adjacent to at least one vertex in

*S*. A partition

*D*= {

*D*

_{1},

*D*

_{2}, …,

*D*} of the vertex set of

_{k}*G*is said to be a domatic partition or simply a

*d*-partition of

*G*if each class

*D*of

_{i}*D*is a dominating set in

*G*. The maximum cardinality taken over all

*d*-partitions of

*G*is called the domatic number of

*G*denoted by

*d*(

*G*). A graph

*G*is said to be domatically critical or

*d*-critical if for every edge

*x*in

*G*,

*d*(

*G*–

*x*) <

*d*(

*G*), otherwise

*G*is said to be domatically non

*d*-critical. The embedding index of a non

*d*-critical graph

*G*is defined to be the smallest order of a

*d*-critical graph

*H*containing

*G*as an induced subgraph denoted by

*θ*(

*G*) . In this paper, we find the

*θ*(

*G*) for the Barbell graph, the Lollipop graph and the Tadpole graph.