The Semi-Image Neighbouhood Block Graph
Crossing Number and Forbidden Subgraphs

K M Niranjan

doi:https://doi.org/10.14445/22315373/IJMTT-V68I4P509

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 68 | Issue 4 | Year 2022 | Article Id. IJMTT-V68I4P509 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I4P509

The Semi-Image Neighbouhood Block Graph Crossing Number and Forbidden Subgraphs

K M Niranjan

Received	Revised	Accepted
13 Mar 2022	15 Apr 2022	28 Apr 2022

Abstract

Let 𝐺 = (𝑉,E) 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. We characterize graphs whose semi-image neighbourhood block graphs are never has crossing number k (k=1 or 2). Also we prove that the semi-image neighbouhood block graph of a graph which are planar and outerplanar in terms of forbidden subgraphs.

Keywords

Semi-Iimage Neighbourhood, Block, Crossing Number, Forbidden, Minimally Nonouterplanar.

References

[1] Basavarajappa N S, Shanmukha M C, Niranjan K M and Shilpa K C, Dakshayani Indices on Carbon and Boron Nitride Nanotubes. 9(4) (2020) 1680– 168.
[2] F.Harary, Graph Theory, Addison Wesley, Reading Mass. (1969).
[3] R S Indumati, M R Rajesh Kanna, H L, Parashivamurthy,Manjula C Gudgeri, Niranjan K M, Topological Indices of 2- Deoxy-D-Glucose for Covid-19, Journal of the Maharaja Sayajirao University of Baroda. 55(2) (2021) 368-374.
[4] V.R.Kulli,On Minimally Nonouterplanargraphs.Proc. Indian.Nat.Sci.Acad. 41 (1975) 275- 280
[5] V.R. Kulli, The Semitotal Block Graph and Total-Block Graph of a Graph of a Graph, Indian J. Pure Appl. Math. 7 (1976) 625-630.
[6] V.R. Kulli and D.G.Akka, Traversability and Planarity of Semitotal Block Graphs, J Math. and Phy. Sci. 12 (1978) 177-178.
[7] V.R.Kulli and D.G.Akka, Traversability and Planarity of Total Block Graphs, J. Mathematical and Physical Sciences. 11 (1977) 365-375.
[8] V.R. Kulli and D.G.Akka, On Semientire Graphs, J. Math. and Phy. Sci. 15 (1981) 585-589.
[9] V.R.Kulli and D.G.Akka,Characterization of Minimally Nonouterplanar Graphs. J.KarnatakUniv.Sci. 22 (1977) 67-73.
[10] V R Kulli, B.Janakiram, K M Niranjan, The Dominating Graph, Graph Theory Notes of New York. 46 (2004) 5-8.
[11] V R Kulli, B Janakiram, K M Niranjan, The Vertex Minimal Dominating Graph, Acta CienciaIndica. Mathematics. 28(3) (2002) 435-440.
[12] V.R. Kulli and K.M.Niranjan, The Semi-Splitting Block Graph of a Graph, Journal of Scientific Research. 2(3) (2010) 485- 488.
[13] V. R. Kulli, B. Basavanagoud and K. M. Niranjan, Quasi-total Graphs with Crossing Numbers, Journal of Scientific Research. 2(2) 257-263 (2010)
[14] V.R. Kulli and K.M.Niranjan, On Minimally Nonouterplanarity of the Semi-Total (Point) Graph of a Graph, J. Sci. Res. 1(3) (2009) 551- 557.
[15] V. R. Kulli and K. M. Niranjan,On Minimally Nonouterplanarity of a Semi Splitting Block Graph of a Graph, International Journal of Mathematics Trends and Technology (IJMTT). 66(7) (2020).
[16] V.R. Kulli and K.M.Niranjan, The Semi-Splitting Block Graphs with Crossing Numbers, Asian Journal of Current Research. 5(1) (2020) 9-16.
[17] V.R.Kulli and K M Niranjan, The Semi-Image Neighbourhood Graph of a Graph, Asian Journal of Mathematics and Computer Research. 27(2) (2020) 36-41.
[18] VR.Kulli .and K.M Niranjan., The Total Closed Neighbourhood Graphs with Crossing Number Three and Four, Journal of Analysis and Computation. 1(1) (2005) 47- 56.
[19] K.M Niranjan., P Nagaraja. and VLokesh., Forbidden Subgraphs for Graphs with Quasi-total Graphs of Crossing Numner≤2,Journal of Intellgemt Systems Research. 2(21) (2008) 109-113.
[20] Maralabhavi, Y.B. Venkanagouda M. Goudar and Anupama, S.B., Some Domination Parameters on Jump Graph, International Journal of Pure and Applied Mathematics. 113 (2017) 47-55.
[21] Maralabhavi, Y.B. Anupama, S.B. and Venkanagouda M. Goudar, Domination Number of Jump Graph, International Mathematical Forum, Hikari Publishing Ltd. 8 (2013) 753-758.
[22] M.H.Muddebihal, Usha.P and Milind S.C, Image Neighbourhood Graph of Graph, The Mathematics Education. 36(2) (2002).
[23] K.M Niranjan, Forbidden Subgraphs for Planar and Outer Planar Interms of Blict Graphs, Journal of Analysis and Computation. 2(1) (2006) 19-22.
[24] K M Niranjan, Rajendra Prasad K C, Venkanagouda M Goudar, DupadahalliBasavaraja, Forbidden Subgraphs for Planar Vertex Semi-Middle Graph, JNNCE Journal of Engineering and Management. 5(2) (2022) 44-47.
[25] K. M Niranjan, Radha R. Iyer, Biradar M. S, Dupadahalli Basavaraja, The Semi-Splitting Block Graphs with Crossing Numbers Three and Forbidden Subgraphs for Crossing Number One, Asian Journal of Current Research. 5(1) (2020) 25-32.
[26] K.M Niranjan , Nagaraja P, Lokesh V, Semi-Image Neighborhood Block Graphs with Crossing Numbers, Journal of Scientific Research. 5(4) (2013) 295-299.
[27] Rajanna N E and Venkanagouda M Goudar, Pathos Vertex Semientire Block Graph, International Journal of Mathematics Trends and Technology. 7(2) (2014) 103-105.
[28] M A Rajan, V Lokesha and K M Niranjan, On study of Vertex of Graph Operations, J Sci. Res. 3(2) (2011) 291-301.
[29] Rajendra Prasad K C, Niranjan K M and Venkanagouda M Goudar, Edge Semi-Middle Graph of a Graph, (submitted).
[30] Rajendra Prasad KC, Venkanagouda M. Goudar and Niranjan K M, Pathos Edge Semi-Middle Graph of a Tree, (submitted).
[31] Rajendra Prasad KC, Venkanagouda M. Goudar and Niranjan KM, Pathos Vertex Semi-Middle Graph of a Tree, South East Asian J. of Mathematics and Mathematical Sciences. 16(1) (2020) 171-176.
[32] Rajendra Prasad K C, Venkanagouda M. Goudar and K.M. Niranjan, Pathos Edge Semi-Middle Graph of a Tree, Malaya Journal of Matematik. 8(4) (2020) 2190-2193.
[33] Rajendra Prasad, K.C. Niranjan, K.M. and Venkanagouda M. Goudar, Vertex Semi-Middle Graph of a Graph, Malaya Journal of Matematik. 7 (2019) 786-789.
[34] Rajendra Prasad, K.C. Niranjan, K.M. and Venkanagouda M. Goudar, Vertex Semi-Middle Domination in Graphs, Jour of Adv Research in Dynamical and Control Systems. 12 (2020) 83-89.
[35] M. C. Shanmukha, K. N. Anil Kumar, N. S. Basavarajappa, And K. M. Niranjan, TopologicalIndices on Properties of Line Graph of Subdivision of Plane Graphs. 9(4) (2020) 2121–2135.
[36] Venkanagouda M. Goudar, Pathos Vertex Semientire Graph of a Tree, International Journal of Applied Mathematical Research. 1(4) (2012) 666-670.
[37] Venkanagouda M. Goudar, K. S. Ashalatha, Venkatesha, M. H. Muddebihal, On the Geodetic Number of Line Graph, Int. J. Contemp. Math. Sciences. 7(46) (2012) 2289 – 2295.

Citation :

K M Niranjan, "The Semi-Image Neighbouhood Block Graph Crossing Number and Forbidden Subgraphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 4, pp. 52-58, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I4P509