<p style='text-indent:20px;'>We give two methods for a construction of self-orthogonal linear codes from equitable partitions distance-regular graphs. By applying these methods, we construct the graph unitals in <inline-formula><tex-math id="M1">\begin{document}$ PG(2,4) $\end{document}</tex-math></inline-formula> and only known strongly regular with parameters id=...

We construct a l-factorizalion of the complement .E, of the linear Hamming code of length m:m,--2'-l in the z-cube Q^, for r ) 2,havitg the following equitable property: its component l-factors intersect each Cayley parallel l-factor of Q^ at a constant number of edges, (namely 2mr-r-t edges). In the way to that construction, we flnd an equitable m,-t-factorization of 2, formed by two factors Q...

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...

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 ...

let g be a graph with p vertices and q edges and a = {0, 1, 2, . . . , [q/2]}. a vertex labeling f : v (g) → a induces an edge labeling f∗ defined by f∗(uv) = f(u) + f(v) for all edges uv. for a ∈ a, let vf (a) be the number of vertices v with f(v) = a. a graph g is said to be vertex equitable if there exists a vertex labeling f such that for all a and b in a, |vf (a) − vf (b)| ≤ 1 and the in...