IJPAM: Volume 106, No. 2 (2016)

A NOTE ON THE GUTMAN INDEX OF JACO GRAPHS

Johan Kok$^1$, C. Susanth$^2$, Sunny Joseph Kalayathankal$^3$
$^1$Tshwane Metropolitan Police Department
City of Tshwane, REPUBLIC OF SOUTH AFRICA
$^2$Department of Mathematics
Vidya Academy of Science and Technology
Thalakkottukara, Thrissur-680501, INDIA
$^3$Department of Mathematics
Kuriakose Elias College
Mannaman, Kottayam-686561, INDIA


Abstract. The concept of the Gutman index, denoted $Gut(G)$ was introduced for a connected undirected graph $G$. In this note we apply the concept to the underlying graphs of the family of Jaco graphs, (directed graphs by definition), and decribe a recursive formula for the Gutman index $Gut(J^*_{n+1}(x))$. We also determine the Gutman index for the trivial edge-joint between Jaco graphs.

Received: November 25, 2015

AMS Subject Classification: 05C12, 05C20, 05C38, 05C40, 05C75

Key Words and Phrases: Gutman index, Jaco graph, edge-joint

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DOI: 10.12732/ijpam.v106i2.21 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: 2016
Volume: 106
Issue: 2
Pages: 583 - 591


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CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).