Abstract. In this paper the structural equivalence of union, intersection ring sum and decomposition of semigraphs are explored by using the various types of isomorphisms such as isomorphism, ev-isomorphism, a-isomorphism and e-isomorphism for G_{e}, G_{a} and G_{ca}. We establish various types of binary operations in semigraphs.

Periodical:

Bulletin of Mathematical Sciences and Applications (Volume 18)

Pages:

11-22

DOI:

10.18052/www.scipress.com/BMSA.18.11

Citation:

P. R. Hampiholi and M. M. Kaliwal, "Operations on Semigraphs", Bulletin of Mathematical Sciences and Applications, Vol. 18, pp. 11-22, 2017

Online since:

May 2017

Authors:

Keywords:

Distribution:

Open Access

This work is licensed under a

Creative Commons Attribution 4.0 International License

References:

[1] B.Y. Bam, N.S. Bhave, On Some problems of Graph Theory in Semigraphs, Ph. D Thesis, University of Pune.

[2] C. Berge, Graphs and hypergraphs, North-Holland, London, (1973).

[3] C.M. Deshpande, Y.S. Gaidhani, About adjacency matrix of semigraphs, International Journal of Applied Physics and Mathematics. 2(4) (2012).

DOI: 10.7763/ijapm.2012.v2.103[4] C.M. Deshpande, Y.S. Gaidhani, B.P. Athawale, Incidence matrix of a Semigraph, British Journal of Mathematics and Computer Science. 9(1) (2015) 12-20..

DOI: 10.9734/bjmcs/2015/17851[5] D.B. West, Introduction to graph theory, Prentice-Hall of India, New Delhi, (1999).

[6] E. Sampatkumar, Semigraphs and their applications, Technical Report [DST/MS/022/94], Department of Science & Technology, Govt. of India, August, (1999).

[7] F. Harary, Graph theory, Addison-Wesley, Reading MA, (1969).

[8] F. Harary, G.W. Wilcox, Boolean operations on graphs, Math. Scand. 20 (1967) 41-52.

DOI: 10.7146/math.scand.a-10817[9] F. Harary, On the group of composition of two graphs, Duke Math. J. 26 (1959) 29-34.

[10] G. Sabidussi, The composition of graphs, Duke Math. J. 26 (1959) 693-696.

DOI: 10.1215/s0012-7094-59-02667-5[11] G. Sabidussi, The lexicographic product of graphs, Duke Math. J. 28 (1961) 573-578.

DOI: 10.1215/s0012-7094-61-02857-5[12] K. Thiagarajan, J. Padmashree, S. Jeyabharathi, Evolutively finite words on semigraph folding, 3rd International Conference on Applied Mathematics and Pharmaceutical Sciences (ICAMPS'2013) April 29-30, Singapore, (2013).

[13] M. Behzad, G. Chartrand, L. Lesniak-Foster, Graphs and Digraph Wadsworth International Group Belmont, (1979).

[14] N. Deo, Graph theory with applications to engineering and computer science, Prentice Hall of India Private Ltd.

[15] P.R. Hampiholi, J.P. Kitturkar, Partial edge Incidence matrix of semigraph over GF(22), International Journal of Engineering Research and Technology. 3(9) (2014).

[16] P.R. Hampiholi, J.P. Kitturkar, Strong circuit matrix and strong path matrix of a semigraph, Annals of Pure and Applied Mathematics. 10(2) (2015) 247-254.

[17] P.M. Weichsel, The Kronecker product of graphs, Proc. Amer. Math. Soc. 13 (1963) 47-52.

[18] P. Das, Surajit Kr. Nath, Factorization in semigraphs, International Journal of Mathematical Sciences and Engineering Applications. 5(VI) (2011).

[19] P. Das, Surajit Kr. Nath, The genus of semigraphs, International Journal of Mathematical Sciences and Engineering Applications. 5(V) (2011).

[20] S. Gomathi, R. Sundareswaran, V. Swaminathan, (m, e)-domination in semigraphs, Electronic Notes in Discrete Mathematics. 33 (2009) 75-80.

DOI: 10.1016/j.endm.2009.03.011[21] S.S. Kamath, R.S. Bhat, Domination in semigraphs, Electronic Notes in Discrete Mathematics. 15 (2003) 106-111.

DOI: 10.1016/s1571-0653(04)00548-7[22] S.S. Kamath, S.R. Hebbar, Strong and weak domination, full sets and domination balance in semigraph, Electronic Notes in Discrete Mathematics and Computer Science. 9(1) (2015) 12-20.

DOI: 10.1016/s1571-0653(04)00549-9[23] Y.B. Venkatakrishnan, V. Swaminathan, Bipartite theory of semigraphs, WSEAS Transactions on Mathematics. 11(1) (2012) 1-9.

[24] Y.B. Venkatakrishnan, V. Swaminathan, Hyper domination in bipartite semigraphs, WSEAS Transactions on Mathematics. 10(11) (2012).