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Sajana, Shaik
- On the Complement of the Intersection Graph of Zero-Divisors of the Ring Zn
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Authors
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1 Department of Mathematics, S.V. University, Tirupati, A.P., -517502, IN
1 Department of Mathematics, S.V. University, Tirupati, A.P., -517502, IN
Source
Research Journal of Science and Technology, Vol 9, No 3 (2017), Pagination: 379-384Abstract
For the ring of integers modulo π, we study the complement of the intersection graph of zero-divisors is denoted by πΊπβ² (ππ)Μ and is defined as a simple undirected graph whose vertices are the set of all nonzero zero-divisors of the ring ππ and in which two distinct vertices are joined by an edge if and only if their corresponding principal ideals have zero intersection. We determine the necessary and sufficient condition for adjacency of vertices in the graph πΊπβ² (ππ)Μ . Also, we investigate the connectedness and further calculate the radius and diameter of the graph πΊπβ² (ππ)Μ for all characterizations of π.Keywords
Intersection Graph, Zero-Divisors, Principal Ideal, Connected Graph, Eccentricity, Radius, Diameter.
References
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- Sajana Shaik, Bharathi D., Srimitra K.K., On the Reduced Intersection Graph of a Ring ππ, International Journal of Advanced Research in Computer Science, 2017, Vol. 8, No. 6, July (Special Issue III), 200-202.
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- On the Signed Mobius Graph for β0β
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Authors
Affiliations
1 Department of Mathematics, S. V. University, Tirupati β 517502, Andhra Pradesh, IN
1 Department of Mathematics, S. V. University, Tirupati β 517502, Andhra Pradesh, IN
Source
Research Journal of Science and Technology, Vol 9, No 4 (2017), Pagination: 521-524Abstract
The signed graphs are rapidly developed in the recent years. A Sign graph is a graph in which each edge is assigned with either positive (+) sign or negative (-) sign. In this paper, we define the Signed Mobius graph for β0β by giving the signs to the edges of the graph of Mobius function for β0β by using the Mobius function value of the vertex. Here we study some properties of a sign graph to this Signed Mobius graph for β0β and we calculate the chromatic number of the Signed Mobius Graph for β0β.Keywords
Mobius Function, Graph of Mobius Function, Sign Function, Signed Mobius Graph, Balanced, Chromatic Number.References
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