Weighted adjacency matrix of a semigraph and its spectral analysis
Weighted adjacency matrix of a semigraph and its spectral analysis / H.N. Ramaswamy, N. Ravikumar
p. 7-30 ; 26 cm
수록자료: Advanced studies in contemporary mathematics. Jangjeon Research Institute for Mathematical Sciences & Physics. Vol.27 no.1(2017 January), p. 7-30 27:1<7 ISSN 1229-3067 저자: H.N. Ramaswamy, Department of Studies in Mathematics, University of Mysore 저자: N. Ravikumar, Department of Mathematics, Government First Grade College
In this paper we introduce weighted adjacency matrix W(G) of a semigraph G study the related spectral properties similar to the spectral properties of the adjacency matrix of graphs. We prove Sachs type theorem by interpreting first few coefficients of the characteristics polynomial of W(G) in terms of the semigraph parameters. We extend Harary formula for the determinant of the adjacency matrix of graphs to the weighted adjacency matrix of semigraphs. We find bounds for eigenvalues and energy for certain classes of semigraphs.