The concept of the incidence chromatic number of a graph was introduced by Brualdi and Massey (1993). They conjectured that every graph G can be incidence colored with ∆(G) + 2 colors. In this paper, we calculate the incidence chromatic numbers of the complete k-partite graphs and give the incidence chromatic number of three infinite families of graphs.

Landslide is one of the common hazards occurring globally and Malaysia is not spared as well. Over the past four decades, Malaysia has played host to a number of landslide incidents, resulting in significant loss of lives and damage to property. The magnitude of landslide destruction is quite high in Malaysia. A survey has been carried out on 143 respondents in selected areas. This paper presen...

We prove three theorems giving extremal bounds on the incidence structures determined by subsets of the points and blocks of a balanced incomplete block design (BIBD). These results generalize and strengthen known bounds on the number of incidences between points and m-flats in affine geometries over finite fields. First, we show an upper bound on the number of incidences between sufficiently l...

We show that n arbitrary circles in the plane can be cut into O(n) arcs, for any ε > 0, such that any pair of arcs intersect at most once. This improves a recent result of Tamaki and Tokuyama [20]. We use this result to obtain improved upper bounds on the number of incidences between m points and n circles. An improved incidence bound is also obtained for graphs of polynomials of any constant m...

Edge-fuzzy graphs constitute an essential modeling paradigm across a broad spectrum of domains ranging from artificial intelligence to computational neuroscience and social network analysis. Under this model, fundamental graph properties such as edge length and graph diameter become stochastic and as such they are consequently expressed in probabilistic terms. Thus, algorithms for fuzzy graph a...

A new method to clustering analysis, which is based on integration of graph theoretical method and fuzzy objective fimction algorithm, is developed. The connectivity mritriv derived from fuzzy limited neighborhood graph and the measurement for similarity and dissimilarity a re utilized to build a new fuzzy objective function that iinifles global data distribution and local spatial information. ...