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On colorings of strongly multiplicative and strongly quotient graphs
C. Adiga,R .K. Zaferani 장전수학회 2006 Advanced Studies in Contemporary Mathematics Vol.13 No.2
Computations of the chromatic number Â(G), the clique number !(G), the cardinality of maximal independent set (G) and the cardinality of minimum de¯ning set d(G; Â) for general graph is difficult. In this paper, we obtain two upper bounds and a lower bound for Â(G) where G is a strongly multiplicative graph of order n. If G is a strongly quotient graph of order n, we provide a lower bound for Â(G), and establish that !(G) = 1+¼(n):We also determine the size of a maximal independent set and minimum defining set of a strongly quotient graph of order n.
Upper bounds for energy of a graph
C. Adiga,R.K. Zaferani 장전수학회 2008 Advanced Studies in Contemporary Mathematics Vol.16 No.2
The energy of a graph G is defined as the sum of absolute values of theeigenvalues of the graph G and is denoted by E(G). In this paper we obtaintwo eigenvalues of a strongly quotient graph SQG with n vertices and maximum number of edges and use them to establish an upper bound for energyof SQG.