International Journal of Mathematics and Soft Computing

1-6

Authors: Paul Manuel, Indra Rajasingh, Bharathi Rajan ,R. Prabha

The all-ones problem is an NP-complete problem introduced by Sutner [11], with wide applications in linear cellular automata. In this paper, we solve the all-ones problem for some of the widely studied architectures like binomial trees, butterfly, and benes networks.

11-24

Authors: S K Vaidya, P L Vihol

Let $G=(V(G),E(G))$ be a connected graph and let $d(u,v)$ denote the distance between any two vertices in $G$. The maximum distance between any pair of vertices is called the diameter of $G$ denoted by $diam(G)$. A radio labeling( or multilevel distance labeling) for $G$ is an injective function $f:V(G) \longrightarrow N\cup\{0\}$ such that for any vertices $u$ and $v$, $|f(u)-f(v)| \geq diam(G)-d(u,v)+1$. The span of $f$ is the largest number in $f(V)$. The radio number of $G$, denoted by $r_n(G)$ is the minimum span of a radio labeling of $G$. In this paper we determine upper bounds of radio numbers for cycle with chords and $n/2$-petal graph. Further the radio number is completely determined for the split graph and middle graph of cycle $C_{n}$.

35-42

Authors: A.O. Adesanya, M.R. Odekunle, A.O. Adeyeye

A method of collocation and interpolation of the power series approximate solution at some grid and off-grid points is considered to generate a continuous linear multistep method for the solution of general second order initial value problems at constant step size. We use continuous block method to generate independent solutions which serves as predictors at selected points within the interval of integration. The efficiency of the proposed method was tested and was found to compete favorably with the existing methods.

49-54

Authors: J. Joseline Manora, V.Swaminathan

In this paper we deal with Nordhaus-Gaddum type results in majority domination number of $G$ and $ \overline G $ and also majority domatic number of $G$ and $\overline G$. We also establish bounds for $\gamma_M(G) + d_M (G)$ and $\gamma_M(G) d_M (G)$.

67-74

Authors: K Vaidya, C M Barasara

A binary vertex labeling of graph $ G $ with induced edge labeling $ f^{*}:E(G) \rightarrow \{0,1\} $ defined by $ f^{*}(e=uv)=f(u)f(v) $ is called a \textit{product cordial labeling} if $ \vert v_{f}(0) - v_{f}(1) \vert \leq 1 $ and $ \vert e_{f}(0) - e_{f}(1) \vert \leq 1 $. A graph is called \textit{product cordial} if it admits product cordial labeling. We prove that the shell admits a product cordial labeling. Sundaram et al.\cite{Sundaram1} proved that if a graph with $p$ vertices and $ q$ edges with $ p \geq 4 $ is product cordial then $ q \leq \dfrac{p^{2}-1}{4} + 1 $. We present here some families of graphs which satisfy this condition but not product cordial.

79-83

Authors: Selvam Avadayappan, M. Muthuchelvam

A connected graph is called neighbourly irregular (NI) if it contains no edge between the vertices of the same degree. In this paper we determine the upper bound for chromatic number of a neighbourly irregular graph. We also prove some results on neighbourly irregular graphs and its chromatic number.

95-102

Authors: S. Pious Missier A. Robert

In this paper we define the semi*-border, semi*-frontier and semi*-exterior of a subset of a topological space and study some of their properties.

1 - 8

Authors: M. Sambasiva Rao

In this paper we derive some sufficient conditions for a prime ideal of a distributive lattice to become an O-ideal. A set of equivalent conditions are established for every O-ideal to become an annihilator ideal. An equivalency is obtained between prime O-ideals and minimal prime ideals of a distributive lattice. Finally, the concept of co-maximality is introduced and obtained that any two distinct prime O-ideals of a distributive lattice are co-maximal.

21-24

Authors: I. Sahul Hamid, Mayamma Joseph, V.M. Abraham

A \emph{decomposition} \quad of a graph \quad $G$ is a collection $\psi=\{H_{1}, H_{2}, \ldots, H_{k}\}$ of subgraphs of $G$ such that every edge of $G$ belongs to exactly one $H_{i}$. The decomposition $\psi$ is called a \emph{path decomposition} of $G$ if each $H_{i}$ is a path in $G$. Several studies have been undertaken on path decompositions by imposing certain conditions on the paths considered in the decomposition of the graph where the primary objective is to obtain the minimum number of paths required for a certain type of decomposition for a given graph. A path decomposition $\psi$ such that the paths in $\psi$ are induced as well as of same parity is defined as an \emph{equiparity induced path decomposition}. The minimum number of paths in such a decomposition of a graph $G$ is called the \emph{equiparity induced path decomposition number} of $G$ and is denoted by $\pi_{pi}(G)$. In this paper we determine the value of $\pi_{pi}$ for trees of even size.

35-49

Authors: M.A.Perumal, S.Navaneethakrishnan, A.Nagarajan, S. Arockiaraj

Let $G$ be a $(p,q)$ - graph. A bijective function $f:V(G)\cup E(G)\rightarrow \{1,2,...,p+q\}$ such that $f(uv)=\left\vert f(u)-f(v) \right\vert$ for every edge $uv\ \epsilon \ E(G)$ is said to be a super graceful labeling. A graph $G$ is called a super graceful graph if it admits a super graceful labeling. In this paper, we show that the graphs $P_n, P_m \odot nK_{1}, P^{+}_{n}-e_{0}$, and $C_n $ are super graceful graphs.

57-63

Authors: M. T. Rahim, M. Farooq, M. Ali, S. Jan

The \emph{radio number} of $G$, $rn(G)$, is the minimum possible span. Let $d(u,v)$ denote the \emph{distance} between two distinct vertices of a connected graph $G$ and $diam(G)$ be the \emph{diameter} of $G$. A \emph{radio labeling} $f$ of $G$ is an assignment of positive integers to the vertices of $G$ satisfying $d(u,v)+|f(u)-f(v)|\geq diam(G)+1$. The largest integer in the range of the labeling is its span. In this paper we show that $rn(J_{t,n})\geq\left\{ \begin{array}{ll} \frac{1}{2}(nt^{2}+2nt+2n+4), & \hbox{when t is even;} \\ \frac{1}{2}(nt^{2}+4nt+3n+4), & \hbox{when t is odd.} \end{array} \right.$\\ \noindent Further the exact value for the radio number of $J_{2,n}$ is calculated.

75-82

Authors: Muhammad Kamran Siddiqui

In this paper, we study the total edge irregularity strength of some well known graphs. An edge irregular total $k$-labeling $\varphi: V\cup E \to \{ 1,2, \dots, k \}$ of a~graph $G=(V,E)$ is a~labeling of vertices and edges of $G$ in such a~way that for any different edges $xy$ and $x'y'$ their weights are distinct. The total edge irregularity strength $tes(G)$ is defined as the minimum $k$ for which $G$ has an~edge irregular total $k$-labeling. Also, we determine the exact value of the total edge irregularity strength of subdivision of star $S_n.$

93-98

Authors: Albert William, A. Shanthakumari

Butterfly network is the most popular bounded-degree derivative of the hypercube network. The benes network consists of back-to-back butterflies. In this paper, we obtain the minimum vertex-disjoint cycle cover number for the odd dimensional butterfly networks and prove that it is not possible to find the same for the even dimensional butterfly networks and benes networks. Further we obtain the minimum edge-disjoint cycle cover number for butterfly networks.

109-117

Authors: T.S.R. Murthy, D. Siva Rama Krishna, G.V.S. Raju

In this paper, we study single server bulk service queuing process in which customers are served in varying batch size and obtain various characteristics of the systems.