Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897750 | Linear Algebra and its Applications | 2018 | 26 Pages |
Abstract
Let G=(V,E) be a simple graph of order n and size m, with vertex set V(G)={v1,v2,â¦,vn}, without isolated vertices and sequence of vertex degrees Î=d1â¥d2â¥â¯â¥dn=δ>0, di=dG(vi). If the vertices vi and vj are adjacent, we denote it as vivjâE(G) or iâ¼j. With TI we denote a topological index that can be represented as TI=TI(G)=âiâ¼jF(di,dj), where F is an appropriately chosen function with the property F(x,y)=F(y,x). A general extended adjacency matrix A=(aij) of G is defined as aij=F(di,dj) if the vertices vi and vj are adjacent, and aij=0 otherwise. Denote by fi, i=1,2,â¦,n the eigenvalues of A. The “energy” of the general extended adjacency matrix is defined as ETI=ETI(G)=âi=1n|fi|. Lower and upper bounds on ETI are obtained. By means of the present approach a plethora of earlier established results can be obtained as special cases.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Kinkar Ch. Das, Ivan Gutman, Igor MilovanoviÄ, Emina MilovanoviÄ, Boris Furtula,