IJPAM: Volume 107, No. 1 (2016)


Johan Kok$^1$, N.K. Sudev$^2$, K.P. Chithra$^2$
$^1$Tshwane Metropolitan Police Department
City of Tshwane, SOUTH AFRICA
$^2$Department of Mathematics
Vidya Academy of Science & Technology
Thrissur, INDIA
$^3$Naduvath Mana, Nandikkara
Thrissur, 680301, INDIA

Abstract. A primitive hole of a graph $G$ is a cycle of length $3$ in $G$. The number of primitive holes in a given graph $G$ is called the primitive hole number of that graph $G$. The primitive degree of a vertex $v$ of a given graph $G$ is the number of primitive holes incident on the vertex $v$. In this paper, we introduce the notion of Pythagorean holes of graphs and initiate some interesting results on Pythagorean holes in general as well as results in respect of set-graphs and Jaco graphs.

Received: February 12, 2016

AMS Subject Classification: 05C07, 05C20, 05C38

Key Words and Phrases: set-graphs, Jaco graphs, primitive hole, Pythagorean hole, graphical embodiment of a Pythagorean triple

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DOI: 10.12732/ijpam.v107i1.15 How to cite this paper?

International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 107
Issue: 1
Pages: 187 - 200

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