A stable set in a graph G is a set of pairwise non-adjacent vertices and α(G) is the size of a maximum stable set in the graph G. The polynomial I(G; x) = s0 + s1x + s2x + ... + sαx, α = α(G), is called the independence polynomial of G (Gutman and Harary, 1983), where sk is the number of stable sets of cardinality k in G. I(G; x) is partial unimodal if the sequence of its coefficients (sk) is p...

Scope and Purpose { One of the main characteristics of a neighbourhood structure imposed on the solution set of a combinatorial optimization problem is the diameter of the corresponding neighbourhood graph. The diameter reeects the 'closeness' of one solution to another. We study the diameter of the neighbourhood graph of some exponential size neighbourhood structure for the TSP and show that t...

In graph theory, the Helly property has been applied to families of sets, such as cliques, disks, bicliques, and neighbourhoods, leading to the classes of clique-Helly, disk-Helly, biclique-Helly, neighbourhood-Helly graphs, respectively. A natural question is to determine for which graphs the corresponding Helly property holds, for every induced subgraph. This leads to the corresponding classe...

We study the topology of polynomial functions by deforming them generically. We explain how the non-conservation of the total “quantity” of singularity in the neighbourhood of infinity is related to the variation of topology in certain families of boundary singularities along the hyperplane at infinity. 2000 Math. Subj. Class. 32S30, 14D05, 32S40, 58K60, 14B07, 58K10, 55R55.

A multivariable polynomial model is introduced to describe n-state spatio-temporal systems. Based on this model, a new neighbourhood detection and transition rules determination method is proposed. Simulation results illustrate that the new method performs well even when the patterns are corrupted by static and dynamical noise.

Neighbourhood in many Nigerian cities had been designed without proper consideration of design principles, which invariably affect the residents’ quality of life. This s‌tudy assessed the experts' and residents’ perception of design correlates of neighbourhood quality in the urban area of Ibadan. Data were obtained from both primary and secondary sources. A ques‌tionnaire survey and direct obse...

In the (k, i)-coloring problem, we aim to assign sets of colors of size k to the vertices of a graph G, so that the sets which belong to adjacent vertices of G intersect in no more than i elements and the total number of colors used is minimum. This minimum number of colors is called the (k, i)-chromatic number. We present in this work a very simple linear time algorithm to compute an optimum (...

Let the vertices of a graph such that every two adjacent vertices have different color is a very common problem in the graph theory. This is known as proper coloring of graphs. The possible number of different proper colorings on a graph with a given number of colors can be represented by a function called the chromatic polynomial. Two graphs G and H are said to be chromatically equivalent, if ...

Graph isomorphism is an important computer science problem. The problem for the general case is unknown to be in polynomial time. The bese algorithm for the general case works in quasi-polynomial time [1]. The solutions in polynomial time for some special type of classes are known. In this work, we have worked with a special type of graphs. We have proposed a method to represent these graphs an...

The paper presents a methodology for designing regression filters. The signal x needs to be locally approximated in the neighbourhood of the instant t using a polynomial of an appropriate degree. The values of the signal derivatives are then determined basing on the polynomial parameters. An advantage of the regression differentiating filters is that it is possible to obtain a filtered signal w...