Status Sum Eigenvalues and Energy of Graphs
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Let G be a simple connected graph with vertex set V (G). The status of a ver- tex v 2 V (G) is denoted by (v) and de ned as the sum of distances from v to all other vertices of G. The status sum matrix of G is de ned by S(G) = [sij ] where sij = (vi) + (vj) if i 6= j, and sij = 0 otherwise. The status sum energy E(G) of a graph G is the sum of the absolute values of the eigenvalues of the status sum matrix. In this paper, we obtain some coecients of the characteristic polynomial (G; ) of status sum matrix. Status sum energies of some well known graphs are obtained and some upper and lower bounds for E(G) are established.
Abstract
Let G be a simple connected graph with vertex set V (G). The status of a ver- tex v 2 V (G) is denoted by (v) and de ned as the sum of distances from v to all other vertices of G. The status sum matrix of G is de ned by S(G) = [sij ] where sij = (vi) + (vj) if i 6= j, and sij = 0 otherwise. The status sum energy E(G) of a graph G is the sum of the absolute values of the eigenvalues of the status sum matrix. In this paper, we obtain some coecients of the characteristic polynomial (G; ) of status sum matrix. Status sum energies of some well known graphs are obtained and some upper and lower bounds for E(G) are established.
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