Bounds for randic and GA indices

The paper establishes some new bounds for Randic and GA indices

Color energy of a unitary Cayley graph

Let G be a vertex colored graph. The minimum number χ(G) of colors needed for coloring of a graph G is called the chromatic number. Recently, Adiga et al. [1] have introduced the concept of color energy of a graph Ec(G) and computed the color energy of few families of graphs with χ(G) colors. In this paper we derive explicit formulas for the color energies of the unitary Cayley graph Xn, the complement of the colored unitary Cayley graph (Xn)c and some gcd-graphs

A note on strongly sum difference quotient graphs

Recently, Adiga and Shivakumar Swamy 1 have introduced the concept of strongly sum difference quotient (SSDQ) graphs and shown that all graphs such as cycles, flowers and wheels are SSDQ graphs. They have also derived an explicit formula for α(n); the maximum number of edges in a SSDQ graphs of order n in terms of Eulers phi function. In this paper, we show that much studied families of graphs such as Mycielskian of the path Pn and the cycle Cn; Cn � Pn; double triangular snake graphs and total graph of Cn are strongly sum difference quotient graphs

Color energy of a graph

In this paper, we introduce the concept of color energy of a graph, E C(G) and compute the color energy EX(G) of few families of graphs with minimum number of colors. It depends on the underlying graph and colors on its vertices. We establish an upper bound and a lower bound for color energy. Also we introduce the concept of complement of a colored graph and compute energies of complement of colored graphs of few families of graphs

On vertex balance index set of some graphs

Let Z2 = {0, 1} and G = (V, E) be a graph. A labeling f : V −→ Z2 induces an edge labeling f ∗ : E −→ Z2 defined by f ∗ (uv) = f(u).f(v). For i ∈ Z2, let vf (i) = v(i) = card{v ∈ V : f(v) = i} and ef (i) = e(i) = card{e ∈ E : f ∗ (e) = i}. A labeling f is said to be vertex-friendly if | v(0)−v(1) |≤ 1. The vertex balance index set is defined by {| ef (0) − ef (1) | : f is vertex-friendly}. In this paper we completely determine the vertex balance index set of Kn, Km,n, Cn × P2 and Complete binary tree

Partition energy of some trees and their generalized complements

Let G = (V, E) be a graph and Pk = {V1, V2, . . . , Vk} be a partition of V . The k-partition energy of a graph G with respect to partition Pk is denoted by EPk (G) and is defined as the sum of the absolute values of k-partition eigenvalues of G. In this paper we obtain partition energy of some trees and their generalized complements with respect to equal degree partition. In addition, we develop a matlab program to obtain partition energy of a graph and its generalized complements with respect to a given partition.Publisher's Versio

ON VERTEX BALANCE INDEX SET OF SOME GRAPHS Communicated by Jamshid Moori

Abstract. Let Z2 = {0, 1} and G = (V, E) be a graph. A labeling f : V −→ Z2 induces an edge labeling f A labeling f is said to be vertex-friendly if | v(0) − v(1) |≤ 1. The vertex balance index set is defined by {| e f (0) − e f (1) | : f is vertex-friendly}. In this paper we completely determine the vertex balance index set of Kn, Km,n, Cn × P2 and Complete binary tree