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.