TY - JOUR
ID - 5573
TI - Randic incidence energy of graphs
JO - Transactions on Combinatorics
JA - TOC
LA - en
SN - 2251-8657
AU - Gu, Ran
AU - Huang, Fei
AU - Li, Xueliang
AD - Nankai University
AD - Center for Combinatorics, Nankai University, Tianjin 300071, China
Y1 - 2014
PY - 2014
VL - 3
IS - 4
SP - 1
EP - 9
KW - Randi'c incidence matrix
KW - Randi'c incidence energy
KW - eigenvalues
DO - 10.22108/toc.2014.5573
N2 - Let $G$ be a simple graph with vertex set $V(G) = {v_1, v_2,ldots, v_n}$ and edge set $E(G) = {e_1, e_2,ldots, e_m}$. Similar to the Randi'c matrix, here we introduce the Randi'c incidence matrix of a graph $G$, denoted by $I_R(G)$, which is defined as the $ntimes m$ matrix whose $(i,j)$-entry is $(d_i)^{-frac{1}{2}}$ if $v_i$ is incident to $e_j$ and $0$ otherwise. Naturally, the Randi'c incidence energy $I_RE$ of $G$ is the sum of the singular values of $I_R(G)$. 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.
UR - https://toc.ui.ac.ir/article_5573.html
L1 - https://toc.ui.ac.ir/article_5573_68f2261c2087d1f09fb34c2f8de4b053.pdf
ER -