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Paper Information

Journal:   TRANSACTIONS ON COMBINATORICS   2014 , Volume 3 , Number 4; Page(s) 1 To 9.
 
Paper: 

RANDIC INCIDENCE ENERGY OF GRAPHS

 
 
Author(s):  GU R., HUANG F., LI X.*
 
* CENTER FOR COMBINATORICS, NANKAI UNIVERSITY, TIANJIN, CHINA
 
Abstract: 

Let G be a simple graph with vertex set V (G) ={v1, v2,… vn} and edge set E (G) = {e1, e2,… em}. Similar to the Randic matrix, here we introduce the Randic incidence matrix of a graph G, denoted by IR (G), which is defined as the n×m matrix whose (I, j) -entry is (di) -1/2 if vi is incident to ej and 0 otherwise. Naturally, the Randic incidence energy IRE of G is the sum of the singular values of IR (G). We establish lower and upper bounds for the Randic incidence energy. Graphs for which these bounds are best possible are characterized. Moreover, we investigate the relation between the Randic incidence energy of a graph and that of its subgraphs. Also we give a sharp upper bound for the Randic incidence energy of a bipartite graph and determine the trees with the maximum Randic incidence energy among all n-vertex trees. As a result, some results are very different from those for incidence energy.

 
Keyword(s): RANDIC INCIDENCE MATRIX, RANDIC INCIDENCE ENERGY, EIGENVALUES
 
References: 
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