TY - JOUR
ID - 3506
TI - Reciprocal degree distance of some graph operations
JO - Transactions on Combinatorics
JA - TOC
LA - en
SN - 2251-8657
AU - Pattabiraman, Kannan
AU - Vijayaragavan, M.
AD - Annamalai University
AD - Thiruvalluvar College of Engineering and Technology
Y1 - 2013
PY - 2013
VL - 2
IS - 4
SP - 13
EP - 24
KW - Reciprocal degree distance
KW - Harary index
KW - Graph operations
DO - 10.22108/toc.2013.3506
N2 - The reciprocal degree distance (RDD), defined for a connected graph $G$ as vertex-degree-weighted sum of the reciprocal distances, that is, $RDD(G) =\sum\limits_{u,v\in V(G)}\frac{d_G(u) + d_G(v)}{d_G(u,v)}.$ The reciprocal degree distance is a weight version of the Harary index, just as the degree distance is a weight version of the Wiener index. In this paper, we present exact formulae for the reciprocal degree distance of join, tensor product, strong product and wreath product of graphs in terms of other graph invariants including the degree distance, Harary index, the first Zagreb index and first Zagreb coindex. Finally, we apply some of our results to compute the reciprocal degree distance of fan graph, wheel graph, open fence and closed fence graphs.
UR - https://toc.ui.ac.ir/article_3506.html
L1 - https://toc.ui.ac.ir/article_3506_bfc02f2003611e70f89d3bbb16913cd1.pdf
ER -