On Distance Energy of Graphs

The D-eigenvalues of a graph G are the eigenvalues of its distance matrix D, and the D-energy ED(G) is the sum of the absolute values of its D-eigenvalues. Two graphs are said to be D-equienergetic if they have the same D-energy. In this note we obtain bounds for the distance spectral radius and D-energy of graphs of diameter 2. Pairs of equiregular D-equienergetic graphs of diameter 2, on p = 3t + 1 vertices are also constructed.

ON DISTANCE ENERGY OF GRAPHS

The D-eigenvalues of a graph G are the eigenvalues of its distance matrix D, and the D-energy ED(G) is the sum of the absolute values of its D-eigenvalues. Two graphs are said to be D-equienergetic if they have the same D-energy. In this note we obtain bounds for the distance spectral radius and D-energy of graphs of diameter 2. Pairs of equiregular D-equienergetic graphs of diameter 2, on p = 3t + 1 vertices are also constructed.

Study on the determination of molecular distance in organic dye mixtures using dual beam thermal lens technique

A sensitive method based on the principle of photothermal phenomena to study the energy transfer processes in organic dye mixtures is presented. A dual beam thermal lens method can be very effectively used as an alternate technique to determine the molecular distance between donor and acceptor in fluorescein–rhodamine B mixture using optical parametric oscillator.

Strongly distance-balanced graphs and graph products

A graph G is strongly distance-balanced if for every edge uv of G and every i 0 the number of vertices x with d.x; u/ D d.x; v/ 1 D i equals the number of vertices y with d.y; v/ D d.y; u/ 1 D i. It is proved that the strong product of graphs is strongly distance-balanced if and only if both factors are strongly distance-balanced. It is also proved that connected components of the direct product of two bipartite graphs are strongly distancebalanced if and only if both factors are strongly distance-balanced. Additionally, a new characterization of distance-balanced graphs and an algorithm of time complexity O.mn/ for their recognition, wheremis the number of edges and n the number of vertices of the graph in question, are given

Equal opportunity networks, distance-balanced graphs, and Wiener game

Given a graph G and a set X ⊆ V(G), the relative Wiener index of X in G is defined as WX (G) = {u,v}∈X 2  dG(u, v) . The graphs G (of even order) in which for every partition V(G) = V1 +V2 of the vertex set V(G) such that |V1| = |V2| we haveWV1 (G) = WV2 (G) are called equal opportunity graphs. In this note we prove that a graph G of even order is an equal opportunity graph if and only if it is a distance-balanced graph. The latter graphs are known by several characteristic properties, for instance, they are precisely the graphs G in which all vertices u ∈ V(G) have the same total distance DG(u) = v∈V(G) dG(u, v). Some related problems are posed along the way, and the so-called Wiener game is introduced.

Challenges Faced by Kerala Tourism Industry

Tourism being a smokeless industry is now a multi-billion, multi-sectoral and multi-dimensional activity in the world. Twenty first century tourism has reached up to space when a Russian rocket carried the space vehicle of Dennis Tito, an American businessman and the world’s first space tourist, to the space station. Time is not too far to carry tourists to moon and other planets in specially launched vehicles. Tourism is being considered as an agent of social change bridging gaps among nations, regions and people and helping them to open up. It is a promoter of development-material and spiritual both at macro and micro level. The General Assembly of the United Nations, in designating the year 1967 as ‘International Tourism Year’ recognized the importance of international travel as a means of fostering understanding among people, and giving them a knowledge of the rich heritage of the past civilizations, a better appreciation of the values of different cultures, thus contributing to the strengthening of world peace. It adopted the theme “Tourism-Passport to peace”. Our veteran national leader and the first Prime Minister of India, Jawaharlal Nehru had said” welcome a tourist and send back a friend” which indicates the need for extending friendly hospitality to the in bound tourists. Modern transportation has removed the obstacles of distance enabling people to appreciate each other engage in the exchange of ideas and commerce. Tourism can help overcome real prejudices and foster bonds. Tourism can be a real force of world peace. Considering the vast and varied potential of tourism in the state and its impact on the economic, social and cultural environment of the state, a detailed study is found to be relevant and imperative