Geodesic
Global domination and neighborhood numbers in Boolean function graph of a graph
Mathematica Bohemica, Tome 130 (2005) no. 3, pp. 231-246

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For any graph $G$, let $V(G)$ and $E(G)$ denote the vertex set and the edge set of $G$ respectively. The Boolean function graph $B(G, L(G), \mathop {\mathrm NINC})$ of $G$ is a graph with vertex set $V(G)\cup E(G)$ and two vertices in $B(G, L(G), \mathop {\mathrm NINC})$ are adjacent if and only if they correspond to two adjacent vertices of $G$, two adjacent edges of $G$ or to a vertex and an edge not incident to it in $G$. In this paper, global domination number, total global domination number, global point-set domination number and neighborhood number for this graph are obtained.
For any graph $G$, let $V(G)$ and $E(G)$ denote the vertex set and the edge set of $G$ respectively. The Boolean function graph $B(G, L(G), \mathop {\mathrm NINC})$ of $G$ is a graph with vertex set $V(G)\cup E(G)$ and two vertices in $B(G, L(G), \mathop {\mathrm NINC})$ are adjacent if and only if they correspond to two adjacent vertices of $G$, two adjacent edges of $G$ or to a vertex and an edge not incident to it in $G$. In this paper, global domination number, total global domination number, global point-set domination number and neighborhood number for this graph are obtained.
DOI : 10.21136/MB.2005.134094
Classification : 05C15, 05C69
Keywords: Boolean function graph; global domination number; neighborhood number 
Janakiraman, T. N.; Muthammai, S.; Bhanumathi, M. Global domination and neighborhood numbers in Boolean function graph of a graph. Mathematica Bohemica, Tome 130 (2005) no. 3, pp. 231-246. doi: 10.21136/MB.2005.134094
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[1] J. Akiyama, T. Hamada, I. Yoshimura: On characterizations of the middle graphs. Tru. Math. (1975), 35–39. | MR

[2] M. Behzad: A criterion for the planarity of the total graph of a graph. Proc. Cambridge Philos. Soc. 63 (1967), 679–681. | MR | Zbl

[3] S. B. Chikkodimath, E. Sampathkumar: Semi total graphs II. Graph Theory Research Report, Karnatak University (1973), 5–9.

[4] E. J. Cockayne, R. M. Dawes, S. T. Hedetniemi: Total domination in graphs. Networks 10 (1980), 211–219. | DOI | MR

[5] T. Hamada, I. Yoshimura: Traversability and connectivity of the middle graph of a graph. Discrete Math. 14 (1976), 247–256. | DOI | MR

[6] F. Harary: Graph Theory. Addison-Wesley, Reading, Mass., 1969. | MR | Zbl

[7] T. N. Janakiraman, S. Muthammai, M. Bhanumathi: On the Boolean function graph of a graph and on its complement. Math. Bohem. 130 (2005), 113–134. | MR

[8] V. R. Kulli, B. Janakiram: The total global domination number of a graph. Indian J. Pure Appl. Math. 27 (1996), 537–542. | MR

[9] O. Ore: Theory of Graphs. Amer. Math. Soc. Colloq. Publ. 38, Providence, 1962. | MR | Zbl

[10] L. Pushpalatha: The global point-set domination number of a graph. Indian J. Pure Appl. Math. 28 (1997), 47–51. | MR | Zbl

[11] E. Sampathkumar: The global domination number of a graph. J. Math. Phys. Sci. 23 (1989), 377–385. | MR | Zbl

[12] E. Sampathkumar, Prabha S. Neeralagi: The neighborhood number of a graph. Indian J. Pure Appl. Math. 16 (1985), 126–132. | MR

[13] E. Sampathkumar, L. Pushpa Latha: Point-set domination number of a graph. Indian J. Pure Appl. Math. 24 (1993), 225–229. | MR

[14] E. Sampathkumar, H. B. Walikar: The connected domination number of a graph. J. Math. Phys. Sci. 13, 607–613. | MR

[15] D. V. S. Sastry, B. Syam Prasad Raju: Graph equations for line graphs, total graphs, middle graphs and quasi-total graphs. Discrete Math. 48 (1984), 113–119. | DOI | MR

[16] H. Whitney: Congruent graphs and the connectivity of graphs. Amer. J. Math. 54 (1932), 150–168. | DOI | MR | Zbl

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