A graph G is r-equitably k-colorable if its vertex set can be partitioned into k independent sets, any two of which differ in size by at most r. The r-equitable chromatic threshold of a graph G, denoted by χr=(G), is the minimum k such that G is r-equitably k -colorable for all k ≥ k. Let G × H denote the Kronecker product of graphs G and H. In this paper, we completely determine the exact valu...

1 Department of Mathematics, University College of Engineering Nagercoil, Anna University of Technology Tirunelveli (Nagercoil Campus), Nagercoil 629 004, Tamil Nadu, India 2 Department of Mathematics, R.V.S College of Engineering and Technology, Coimbatore 641 402, Tamil Nadu, India 3 Department of Mathematics, Sri Shakthi Institute of Engineering and Technology, Coimbatore 641 062, Tamil Nadu...

a graph g is said to have a totally magic cordial labeling with constant c if there exists a mapping f : v (g) ∪ e(g) → {0, 1} such that f(a) + f(b) + f(ab) ≡ c (mod 2) for all ab ∈ e(g) and |nf (0) − nf (1)| ≤ 1, where nf (i) (i = 0, 1) is the sum of the number of vertices and edges with label i. in this paper, we give a necessary condition for an odd graph to be not totally magic cordial and ...

mean labelings are a type of additive vertex labeling. this labeling assigns non-negative integers to the vertices of a graph in such a way that all edge-weights are different, where the weight of an edge is defined as the mean of the end-vertex labels rounded up to the nearest integer. in this paper we focus on mean labelings of some graphs that are the result of the corona operation. in parti...

We confirm the equitable ∆-coloring conjecture for interval graphs and establish the monotonicity of equitable colorability for them. We further obtain results on equitable colorability about square (or Cartesian) and cross (or direct) products of graphs.

A proper vertex coloring of a graph is equitable if the sizes of its color classes differ by at most one. In this paper, we prove that if G is a graph such that for each edge xy ∈ E(G), the sum d(x)+ d(y) of the degrees of its ends is at most 2r + 1, then G has an equitable coloring with r + 1 colors. This extends the Hajnal–Szemerédi Theorem on graphs with maximum degree r and a recent conject...

For several decades, context effects in picture naming and word reading have been extensively investigated. However, researchers have found no agreement on the explanation of the effects. Whereas it has long been assumed that several types of effect reflect competition in word selection (e.g., Levelt, Roelofs, & Meyer, 1999), recently it has been argued that these effects reflect the exclusion ...

An equitable coloring of a graph is a proper vertex coloring such that the sizes of any two color classes differ by at most one. The least positive integer k for which there exists an equitable coloring of a graph G with k colors is said to be the equitable chromatic number of G and is denoted by χ=(G). The least positive integer k such that for any k′ ≥ k there exists an equitable coloring of ...