Health & Environmental Research Online (HERO)


Print Feedback Export to File
7559279 
Journal Article 
Some Eigenvalue Properties and New Bounds for the Energy of Extended Adjacency Matrix of Graphs 
Liu, C; Pan, YG; Dai, L; Li, JP 
2020 
1 
Match (Mülheim an der Ruhr, Germany)
ISSN: 0340-6253 
84 
2 
349-362 
WOS:000545446500006 
Let G be a graph with vertex set V = V(G) = {v(1),v(2), ...,v(n)} and edge set E = E(G). In 1994, Yang et al. proposed the extended adjacency matrix, denoted by A(ex) = A(ex)(G), which is defined that its (i, j)-entry is equal to 1/2 (d(i)/d(j) + d(j)/d(i)) if the vertices v(i) and v(j) are adjacent, and 0 otherwise, where d(i) is the degree of vertex v(i). In this paper, we first derive some new bounds for the extended spectral radius (eta(1)) in terms of some significant graph parameters, such as the minimum and maximum degree of G, the chromatic number (X), the Randic index (R), the modified second Zagreb index (M-2*), the Symmetric Division Deg index (SDD) and so on. Moreover, several eigenvalue properties of extended adjacency matrix are presented. Finally, we characterize some new lower and upper bounds on epsilon(ex).