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A Note on the Integrity of Middle Graphs

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Book cover Discrete Geometry, Combinatorics and Graph Theory (CJCDGCGT 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4381))

Abstract

The integrity I(G) of a noncomplete connected graph G is a measure of network invulnerability and is defined by I(G) =  min {|S| + m(G − S)}, where S and m(G − S) denote the the subset of V and the order of the largest component of G − S, respectively. In this paper, we determine the integrity and some other parameters of middle graphs of some classes of graphs.

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References

  1. Bagga, K., Beineke, L., Goddard, W., Lipman, L., Pippert, R.: A Survey of Integrity. Discrete Applied Math. 37/38, 13–28 (1992)

    Article  MathSciNet  Google Scholar 

  2. Bagga, K., Beineke, L., Lipman, M., Pippert, R.: Edge-Integrity: A Survey. Discrete Math. 124, 3–12 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  3. Barefoot, C.A., Entringer, R., Swart, H.: Vulnerability in Graphs—A Comparative Survey. J.Combin. Math. Combin. Comput. 1, 13–21 (1987)

    MathSciNet  MATH  Google Scholar 

  4. Bauer, B., Tindell, R.: The Connectivities of Middle Graph. J. Combin. Inform. Sys. Sci. 7(1), 54–55 (1982)

    MathSciNet  MATH  Google Scholar 

  5. Bondy, J.A., Murty, U.S.R: Graph Theory with Applications. Macmillan, London (1976)

    Google Scholar 

  6. Clark, L.H., Entringer, R.C., Fellows, M.: Computational Complexity of Integrity. J. Combin. Math. Combin. Comput. 2, 179–191 (1987)

    MathSciNet  MATH  Google Scholar 

  7. Goddard, W., Swart, H.: Integrity in Graphs: Bounds and Basics. J. Combin. Math. Combin.Comput. 7, 139–151 (1990)

    MathSciNet  MATH  Google Scholar 

  8. Hamada, T., Yushimura, I.: Tranversability and Connectivity of the Middle Graph of a Graph. Discrete Math. 14, 247–255 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kratsch, D., Kloks, T., Müller, H.: Measuring the Vulnerability for Classes of Intersection Graphs. Discrete Applied Math. 77(3), 259–270 (1997)

    Article  MATH  Google Scholar 

  10. Dündar, P., Aytac, A.: Integrity of Total Graphs via Certain Parameters. Mathematical Notes 76(5), 665–672 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  11. Vince, A.: The Integrity of a Cubic Graph. Discrete Applied Math. 140, 223–239 (2004)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, P.R. China

    Aygul Mamut & Elkin Vumar

Authors
  1. Aygul Mamut
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  2. Elkin Vumar
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Editor information

Jin Akiyama William Y. C. Chen Mikio Kano Xueliang Li Qinglin Yu

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© 2007 Springer Berlin Heidelberg

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Mamut, A., Vumar, E. (2007). A Note on the Integrity of Middle Graphs. In: Akiyama, J., Chen, W.Y.C., Kano, M., Li, X., Yu, Q. (eds) Discrete Geometry, Combinatorics and Graph Theory. CJCDGCGT 2005. Lecture Notes in Computer Science, vol 4381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70666-3_14

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  • DOI: https://doi.org/10.1007/978-3-540-70666-3_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70665-6

  • Online ISBN: 978-3-540-70666-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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