Open AccessHarary index of the k-th power of a graph
Author(s) -
Guifu Su,
Liming Xiong,
İvan Gutman
Publication year - 2012
Publication title -
applicable analysis and discrete mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.69
H-Index - 26
eISSN - 2406-100X
pISSN - 1452-8630
DOI - 10.2298/aadm121130024s
Subject(s) - mathematics , combinatorics , graph , reciprocal , distance regular graph , graph power , discrete mathematics , line graph , linguistics , philosophy
The k-th power of a graph G, denoted by Gk, is a graph with the same set of vertices as G, such that two vertices are adjacent in Gk if and only if their distance in G is at most k. The Harary index H is the sum of the reciprocal distances of all pairs of vertices of the underlying graph. Lower and upper bounds on H(Gk) are obtained. A Nordhaus-Gaddum type inequality for H(Gk) is also established.
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