SUONAN Renqian1,2， LI Shenggang1
(1 College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710119, Shaanxi, China;2 Department of Mathematics, Qinghai Normal University, Xining 810008, Qinghai, China)
Abstract:
The energy E(G) of a graph G is defined as the sum of the absolute values of the eigenvalues of graph G. Let Tn(n≥4) be a graph obtained from the path Pn=v1v2…vn by joining one pendent vertex to vertex v2 and Tn(vi)1 a graph obtained from the path Pn=v1v2…vn by joining one pendent vertex to the vertex v2 and one pendent vertex to vertex vi, respectively.Tn(vi)1 is abbreviated to n(2,i)1.The energy ordering of the tree n(2,i)1 is solved completely and it is found that there are four cases based on the residues modulus 4 of n. About the tree n(2,i)k1k2 that has similar structure with n(2,i)1, it is conjectured that the energy ordering of n(2,i)k1k2 is similar to that of n(2,i)1.
KeyWords:
graph theory; tree; energy; ordering
