The P3 Intersection Graph

We define a new graph operator called the P3 intersection graph, P3(G)- the intersection graph of all induced 3-paths in G. A characterization of graphs G for which P-3 (G) is bipartite is given . Forbidden subgraph characterization for P3 (G) having properties of being chordal , H-free, complete are also obtained . For integers a and b with a > 1 and b > a - 1, it is shown that there exists a graph G such that X(G) = a, X(P3( G)) = b, where X is the chromatic number of G. For the domination number -y(G), we construct graphs G such that -y(G) = a and -y (P3(G)) = b for any two positive numbers a > 1 and b. Similar construction for the independence number and radius, diameter relations are also discussed.

GALLAI AND ANTI-GALLAI GRAPHS OF A GRAPH

Abstract. The paper deals with graph operators-the Gallai graphs and the anti-Gallai graphs. We prove the existence of a finite family of forbidden subgraphs for the Gallai graphs and the anti-Gallai graphs to be H-free for any finite graph H. The case of complement reducible graphs-cographs is discussed in detail. Some relations between the chromatic number, the radius and the diameter of a graph and its Gallai and anti-Gallai graphs are also obtained.

Synthesis and characterization of eco-friendly inorganic yellow pigments for coloring applications

Research in the fields of ceramic pigments is oriented towards the enlargement of the chromatic set of colors together with a replacement for more expensive and less stable organic pigments. Novel non-toxic inorganic pigments have been required to answer environmental laws to remove elements like lead, chromium, cobalt entering in the composition of usual pigments widely used in paints and plastics. Yellow is particularly an important color in the pigment industry and consumption of yellow exceeds that of any other colored pigments. Apart from this, high infrared reflective pigments are now in great demand for usage in coatings, cement pavements, automotives and camouflage applications. They not only impart color to an object, but also reflect the invisible heat from the object to minimize heat build–up, when exposed to solar radiation. With this in view, the present work aims at developing new functional yellow pigments for these applications. A series of IR reflecting yellow pigments have been synthesized and analyzed for their crystalline structure, morphological, composition and optical characteristics, coloring and energy saving applications