an acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. the acyclic chromatic index of a graph $g$ denoted by $chi_a '(g)$ is the minimum number $k$ such that there is an acyclic edge coloring using $k$ colors. the maximum degree in $g$ denoted by $delta(g)$, is the lower bound for $chi_a '(g)$. $p$-cuts introduced in this paper acts as a powerfu...

{sl Let $[n]={1,dots, n}$ be colored in $k$ colors. A rainbow AP$(k)$ in $[n]$ is a $k$ term arithmetic progression whose elements have different colors. Conlon, Jungi'{c} and Radoiv{c}i'{c} cite{conlon} prove that there exists an equinumerous 4-coloring of $[4n]$ which is rainbow AP(4) free, when $n$ is even. Based on their construction, we show that such a coloring of $[4n]$...

Using the semi-tensor product of matrices, this paper investigates the maximum (weight) stable set and vertex coloring problems of graphs with application to the group consensus of multi-agent systems, and presents a number of new results and algorithms. Firstly, by defining a characteristic logical vector and using the matrix expression of logical functions, an algebraic description is obtaine...

Giriş: Çene-yüz protezlerinin yenilenmesi gerekliliğini doğuran başlıca sebeplerden biri, protezde kullanılan silikon elastomerlerin fiziksel ve mekanik özelliklerinin zayıflamasıdır. Bu özellikler içinde sertlik, protezin çevre doku ile uyumlu hareketini etkilediğinden dokularda irritasyona neden olabildiğinden dolayı önemlidir. Amaç: çalışmanın amacı, çene-yüz protezinde elastomere eklenen re...

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph $G$ denoted by $chi_a '(G)$ is the minimum number $k$ such that there is an acyclic edge coloring using $k$ colors. The maximum degree in $G$ denoted by $Delta(G)$, is the lower bound for $chi_a '(G)$. $P$-cuts introduced in this paper acts as a powerfu...

A fuzzy graph is a symmetric binary fuzzy relation on a fuzzy subset. The concept of fuzzy sets and fuzzy relations was introduced by L.A.Zadeh in 1965cite{zl} and further studiedcite{ka}. It was Rosenfeldcite{ra} who considered fuzzy relations on fuzzy sets and developed the theory of fuzzy graphs in 1975. The concepts of fuzzy trees, blocks, bridges and cut nodes in fuzzy graph has been studi...

We investigate approximate pure Nash equilibria in digraph k-coloring games, where we are given an unweighted directed graph together with a set of k colors. Vertices represent agents and arcs capture their mutual unidirectional interests. The strategy set of each agent v consists of the k colors and the payoff of v in a given state or coloring is given by the number of outgoing neighbors with ...

two sensitive spectrophotometric methods are presented for the assay of repaglinide in bulkdrug and in formulations using methyl orange, as reagents. oxidant by reacting with a fixedamount of either methyl orange and measuring the absorbance at 485.2 nm (method-i) andmeasuring the absorbance at 618.9 nm (method-ii). developed method is based on the formationof extractable colored complex of dru...