Volume 66 | Issue 7 | Year 2020 | Article Id. IJMTT-V66I7P517 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I7P517

Let G = (V) be a simple connected undirected graph with vertex set V and edge set E. The advent of graph theory has played a prominent role in wide variety of engineering applications and optimizes its use in many applications. In this paper, we present here characterize graphs whose semi-splitting block graphs are minimally nonouterplanar.

[1] F.Harary, Graph Theory, Addison Wesley, Reading Mass. (1969).

[2] V.R.Kulli,On minimally nonouterplanar graphs.Proc. Indian.Nat.Sci.Acad. 41 (1975) 275- 280

[3] V.R. Kulli, The semitotal block graph and total-block graph of a graph of a graph, IndianJ. Pure Appl. Math., 7, 625-630 (1976).

[4] V.R. Kulli and K.M.Niranjan, The semi-splitting block graph of a graph, Journal of Scientific Research, 2(3) (2010) 485- 488.

[5] M.S.Biradar, Eulerianity of some graph valued functions, International Journal of Mathematics Trends and Technology, Vol.33 no. 2 (5), 127-129 (2016).

[6] M.S.Biradar and V.R.Kulli, Results on labeled path and its iterated line graphs, Intern. J.Fuzzy Mathematical Archive, Vol. 10, No. 2, 125-129 (2016).

[7] M.S.Biradar and S.S.Hiremath, The total blitact graph of a graph, Intern. J. MathematicalArchive 7 (5), pp 49-54, (2016).

[8] V.R.Kulli, On full graphs, J. Comp. & Math. Sci, vol.(6), 261-267, 5, pp261-267, (2015).

[9] V.R. Kulli, On the plick graph and the qlick graph of a graph, Research Journal, 1, 48-52(1988).

[10] V.R. Kulli and D.G.Akka, Traversability and planarity of semitotal block graphs, J Math.and Phy. Sci., 12, 177-178(1978).

[11] V.R.Kulli and D.G.Akka, Traversability and planarity of total block graphs. J. Mathematical and Physical Sciences, 11, 365-375 (1977).23. 12

[12] V.R. Kulli and D.G.Akka, On semientire graphs, J. Math. and Phy. Sci, 15, 585-589, (1981).

[13] V.R.Kulli and D.G.Akka,Characterization of minimally nonouterplanar graphs. J.Karnatak Univ.Sci. 22 (1977) 67-73.

[14] V.R. Kulli and N.S.Annigeri, The ctree and total ctree of a graph, Vijnana Ganga, 2, 10-24 (1981).

[15] V.R. Kulli and B. Basavanagoud, On the quasivertex total graph of a graph, J. Karnatak University Sci., 42, 1-7 (1998).

[16] V. R. Kulli, B. Basavanagoud and K. M. Niranjan, Quasi-total Graphs with Crossing Numbers, Journal of Scientific Research. 2 (2), 257-263 (2010)

[17] V.R. Kulli and M.S. Biradar, On eulerian blict graphs and blitact graphs, Journal of Computer and Mathematical Sciences, 6(12), 712-717 (2015).

[18] V.R. Kulli and M.S. Biradar, The point block graph of a graph, Journal of Computer and Mathematical Sciences, 5 (5), 476-481 (2014).

[19] V.R. Kulli and M.S. Biradar, The middle blict graph of a graph, International Research Journal of Pure Algebra 5(7), 111-117 (2015).

[20] V.R. Kulli and M.S. Biradar, Planarity of the point block graph of a graph, Ultra Scientist,18, 609-611 (2006).

[21] V.R. Kulli and M.S. Biradar, The point block graphs and crossing numbers, Acta Ciencia Indica, 33(2), 637-640 (2007).

[22] V.R. Kulli and M.S. Biradar, The line splitting graph of a graph. Acta Ciencia Indica, Vol. XXVIII M, No. 3, 435 (2002).

[23] V.R. Kulli and K.M.Niranjan, On minimally nonouterplanarity of the semi-total (point) graph of a graph, J. Sci. Res. 1(3), 551- 557 (2009).

[24] V.R. Kulli and K.M.Niranjan, The semi-splitting block graphs with crossing numbers, Asian Journal of Research.Activites (submitted)

[25] V.R.Kulli and K M Niranjan, The semi-image neighbourhood graph of a graph, Asian Journal of Mathematics and computer research (Accepted)

[26] V.R. Kulli and N.S. Warad, On the total closed neighbourhood graph of a graph, J. Discrete Mathematical Sciences and Cryptography, 4, 109-114 (2001).

[27] M.H.Muddebihal, Usha.P and Milind S.C., Image neighbourhood graph of graph,The Mathematics Education Vol.XXXVI, No.2,2002.

[28] K. M. Niranjan, P. Nagaraja and Lokesh V, Semi-Image Neighborhood Block Graphs with Crossing Numbers, Journal of Scientific Research, 5(2) 295-299. (2013)

[29] Rajendra Prasad K C, Niranjan K M and Venkanagouda M Goudar, Vertex semi-middle graph of a graph, Malaya Journal of Matematik, Vol. 7, No. 4, 786-789, 2019.

[30] Rajendra Prasad KC, Venkanagouda M. Goudar and Niranjan K M, Pathos vertex semi-middle graph of a tree,south east asian j. of mathematics and mathematical sciences, Vol. 16, No. 1 (2020), pp. 171-176.

[31] Rajanna N Eand Venkanagouda M Goudar, Pathos Vertex Semientire Block Graph, International Journal of Mathematics Trends and Technology, Vol.7.,No.2, 103-105,2014

[32] Rajendra Prasad K C, Niranjan K M and Venkanagouda M Goudar, Edge semi-middle graph of a graph, (submitted)

[33] Rajendra Prasad KC, Venkanagouda M. Goudar and Niranjan K M, Pathos edge semi-middle graph of a tree, (submitted)

[34] H.P.Patil and S.Tamga Mari, Proc. Nat. Workshop on Graph Theory and its applications. M.S.Univ., Tirunelveli 121, (1996).

[35] Sampathkumar and H.B.Walikar, J.Karnatak Univ. Sci. 25, 13,(1980-81).

V. R. Kulli, K. M. Niranjan, "On Minimally Nonouterplanarity of a Semi- Splitting Block Graph of a Graph," *International Journal of Mathematics Trends and Technology (IJMTT)*, vol. 66, no. 7, pp. 127-133, 2020. *Crossref*, https://doi.org/10.14445/22315373/IJMTT-V66I7P517