IJPAM: Volume 106, No. 3 (2016)

ON ZAGREB INDICES AND ECCENTRIC
CONNECTIVITY INDEX OF CERTAIN THORN GRAPHS

U. Mary$^1$, A. Kulandai Therese$^2$,
M. Jerlin Seles$^3$, R. Jayasree$^4$, Johan Kok$^4$
$^{1,2,3,4}$Department of Mathematics
Nirmala College For Women
Coimbatore, INDIA
$^4$Tshwane Metropolitan Police Department
City of Tshwane, REPUBLIC OF SOUTH AFRICA


Abstract. The first three Zagreb indices of a graph $G$ denoted, $M_1(G), M_2(G)$ and $M_3(G)$, are well known. Equally well known is the eccentricity connectivity index denoted, $\xi^c(G)$. In this paper we derive closed formula for these indices for thorn cycles, thorn star graphs and thorn complete graphs, respectively. Same is repeated for the eccentricity connectivity index. The further aim of the paper is to emphasize the subtle difference between mathematical induction and immediate induction as equally valid techniques of proof. Valid immediate induction requires the rarely utilised property of many graphs namely, well-defineness.

Received: January 10, 2016

AMS Subject Classification: 05C07, 05C38, 05C75, 05C85

Key Words and Phrases: complete graph, cycle graph, star graph, thorn graph, bushy thorn graph, eccentric connectivity index, Zagreb indices

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DOI: 10.12732/ijpam.v106i3.16 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: 3
Pages: 909 - 921


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