IJPAM: Volume 105, No. 3 (2015)

SCHULTZ AND GUTMAN INDICES FOR
GRAPH COMPLEMENTS

S. Ramakrishnan$^1$, J. Baskar Babujee$^2$
$^1$Department of Mathematics
Sri Sai Ram Engineering College
Chennai 600044, INDIA
$^2$Department of Mathematics
Anna University
Chennai 600025, INDIA


Abstract. A graph $G$ is said to have property (*) [4] if for every pair of its adjacent vertices $u$ and $v$ there exists a vertex $w$ such that $w$ is not adjacent to $u$ and $v$. In this paper we establish an explicit formula to calculate the Schultz and Gutman indices for the complement of any graph $G$ having the above property. As a corollary we obtain the Schultz and Gutman indices for the complement of certain derived graphs.

Received: July 29, 2015

AMS Subject Classification: 05C10, 05C12, 92E10, 94C15

Key Words and Phrases: Gutman index, line graph, Schultz index, subdivision graph, Zagreb index

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DOI: 10.12732/ijpam.v105i3.6 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 105
Issue: 3
Pages: 383 - 392


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