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The order difference interval graph of a group | ||
| Transactions on Combinatorics | ||
| مقاله 6، دوره 1، شماره 2، شهریور 2012، صفحه 59-65 اصل مقاله (723.25 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2012.1588 | ||
| نویسندگان | ||
| P. Balakrishnan* 1؛ R. Kala2 | ||
| 1Department of Mathematics, Manonmaniam Sundaranar University, tirunelveli | ||
| 2Department of Mathematics Manonmaniam Sundaranar University Tirunelveli 627 012, Tamil Nadu, India. | ||
| چکیده | ||
| In this paper we introduce the concept of order difference interval graph $\Gamma_{ODI}(G)$ of a group $G$. It is a graph $\Gamma_{ODI}(G)$ with $V(\Gamma_{ODI}(G)) = G$ and two vertices $a$ and $b$ are adjacent in $\Gamma_{ODI}(G)$ if and only if $o(b)-o(a) \in [o(a), o(b)]$. Without loss of generality, we assume that $o(a) \leq o(b)$. In this paper we obtain several properties of $\Gamma_{ODI}(G)$, upper bounds on the number of edges of $\Gamma_{ODI}(G)$ and determine those groups whose order difference interval graph is isomorphic to a complete multipartite graph. | ||
| کلیدواژهها | ||
| Order difference interval graph؛ unicyclic graph؛ Eulerian؛ gen- erating set | ||
| مراجع | ||
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T. M. Apostol (1998) Introduction to Analytic number theory Narosa Publishing house, New Delhi
F. Harary (1969) Graph Theory Addison-Wesley, Reading, Mass
I. N. Herstein (2003) Topics in Algebra Second edition, John Wiley \& Sons
M. Sattanathan and R. Kala (2009) An Introduction to Order Prime Graph nt. J. Contemp. Math. Sci. 4 (10), 467-474
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