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Abstract
An edge subset F of a connected graph G is a super edge cut if G − F is disconnected and every component of G−F has atleast two vertices. The minimum cardinality of super edge cut is called super edge connectivity number and it is denoted by λ'(G). Every arithmetic graph G = Vn, n not equal to p1 × p2 has super edge cut. In this paper, the authors study super edge connectivity number of an arithmetic graphs G = Vn, n = p_1^a_1 × p_2^a_2 , a1 > 1, a2 ≥ 1, and G = Vn, n = p_1^a_1 × p_2^a_2 × · · · ×p_r^a_r , r > 2, ai ≥ 1, 1 ≤ i ≤ r.
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References
- Bondy and Murty, Graph theory with applications, Macmillan, 1976.
- Esfahanian, A.-H., and Hakimi, S.L., ”On computing a conditional edge-connectivity of a graph”, Information processing letters, 27:4 (1988), 195-199.
- Jun-Ming Xu, and Ke-Li Xu, ”Note on restricted edge-connectivity of graphs”, Discrete Mathematics, 243 (2002) 291-298.
- Mary Jenitha, L., and Sujitha, S., ”The connectivity number of an arithmetic graph”, International journal of Mathematical combinatorics, 1 (2018), 132-136.
- Mary Jenitha, L., Sujitha, S., and Uma Devi, B., ”The average connectivity of an arithmetic graph”, Journal of Computational Information Systems, 15:1 (2019), 204-207
- Mary Jenitha, L., and Sujitha, S., ”Super connected and hyper connected arithmetic graphs”, Malaya Journal of Matematik, S:1 (2020), 243-247.
- Mary Jenitha, L., and Sujitha, S., ”The connectivity number of complement of an arithmetic graph G = Vn”, Proceedings of the national conference on scientific approaches to multidisciplinary research, (2020), 226-230
- Vasumathi, N., and Vangipuram, S., ”Existence of a graph with a given domination Parameter”, Proceedings of the Fourth Ramanujan Symposium on Algebra and its Applications, University of Madras, Madras, (1995), 187-195
References
Bondy and Murty, Graph theory with applications, Macmillan, 1976.
Esfahanian, A.-H., and Hakimi, S.L., ”On computing a conditional edge-connectivity of a graph”, Information processing letters, 27:4 (1988), 195-199.
Jun-Ming Xu, and Ke-Li Xu, ”Note on restricted edge-connectivity of graphs”, Discrete Mathematics, 243 (2002) 291-298.
Mary Jenitha, L., and Sujitha, S., ”The connectivity number of an arithmetic graph”, International journal of Mathematical combinatorics, 1 (2018), 132-136.
Mary Jenitha, L., Sujitha, S., and Uma Devi, B., ”The average connectivity of an arithmetic graph”, Journal of Computational Information Systems, 15:1 (2019), 204-207
Mary Jenitha, L., and Sujitha, S., ”Super connected and hyper connected arithmetic graphs”, Malaya Journal of Matematik, S:1 (2020), 243-247.
Mary Jenitha, L., and Sujitha, S., ”The connectivity number of complement of an arithmetic graph G = Vn”, Proceedings of the national conference on scientific approaches to multidisciplinary research, (2020), 226-230
Vasumathi, N., and Vangipuram, S., ”Existence of a graph with a given domination Parameter”, Proceedings of the Fourth Ramanujan Symposium on Algebra and its Applications, University of Madras, Madras, (1995), 187-195