Harary Index of Product Graphs

K. Pattabiraman; P. Paulraja

Discussiones Mathematicae Graph Theory (2015)

  • Volume: 35, Issue: 1, page 17-33
  • ISSN: 2083-5892

Abstract

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The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. In this paper, the exact formulae for the Harary indices of tensor product G × Km0,m1,...,mr−1 and the strong product G⊠Km0,m1,...,mr−1 , where Km0,m1,...,mr−1 is the complete multipartite graph with partite sets of sizes m0,m1, . . . ,mr−1 are obtained. Also upper bounds for the Harary indices of tensor and strong products of graphs are estabilished. Finally, the exact formula for the Harary index of the wreath product G ○ G′ is obtained.

How to cite

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K. Pattabiraman, and P. Paulraja. "Harary Index of Product Graphs." Discussiones Mathematicae Graph Theory 35.1 (2015): 17-33. <http://eudml.org/doc/271231>.

@article{K2015,
abstract = {The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. In this paper, the exact formulae for the Harary indices of tensor product G × Km0,m1,...,mr−1 and the strong product G⊠Km0,m1,...,mr−1 , where Km0,m1,...,mr−1 is the complete multipartite graph with partite sets of sizes m0,m1, . . . ,mr−1 are obtained. Also upper bounds for the Harary indices of tensor and strong products of graphs are estabilished. Finally, the exact formula for the Harary index of the wreath product G ○ G′ is obtained.},
author = {K. Pattabiraman, P. Paulraja},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {tensor product; strong product; wreath product; Harary index},
language = {eng},
number = {1},
pages = {17-33},
title = {Harary Index of Product Graphs},
url = {http://eudml.org/doc/271231},
volume = {35},
year = {2015},
}

TY - JOUR
AU - K. Pattabiraman
AU - P. Paulraja
TI - Harary Index of Product Graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2015
VL - 35
IS - 1
SP - 17
EP - 33
AB - The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. In this paper, the exact formulae for the Harary indices of tensor product G × Km0,m1,...,mr−1 and the strong product G⊠Km0,m1,...,mr−1 , where Km0,m1,...,mr−1 is the complete multipartite graph with partite sets of sizes m0,m1, . . . ,mr−1 are obtained. Also upper bounds for the Harary indices of tensor and strong products of graphs are estabilished. Finally, the exact formula for the Harary index of the wreath product G ○ G′ is obtained.
LA - eng
KW - tensor product; strong product; wreath product; Harary index
UR - http://eudml.org/doc/271231
ER -

References

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