On the Boolean function graph of a graph and on its complement

T. N. Janakiraman; S. Muthammai; M. Bhanumathi

Mathematica Bohemica (2005)

  • Volume: 130, Issue: 2, page 113-134
  • ISSN: 0862-7959

Abstract

top
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 ) , N I N C ) of G is a graph with vertex set V ( G ) E ( G ) and two vertices in B ( G , L ( G ) , N I N C ) 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 . For brevity, this graph is denoted by B 1 ( G ) . In this paper, structural properties of B 1 ( G ) and its complement including traversability and eccentricity properties are studied. In addition, solutions for Boolean function graphs that are total graphs, quasi-total graphs and middle graphs are obtained.

How to cite

top

Janakiraman, T. N., Muthammai, S., and Bhanumathi, M.. "On the Boolean function graph of a graph and on its complement." Mathematica Bohemica 130.2 (2005): 113-134. <http://eudml.org/doc/249575>.

@article{Janakiraman2005,
abstract = {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 $B(G,L(G),\mathop \{\mathrm \{N\}INC\})$ of $G$ is a graph with vertex set $V(G)\cup E(G)$ and two vertices in $B(G,L(G),\mathop \{\mathrm \{N\}INC\})$ 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 $G$. For brevity, this graph is denoted by $B_1(G)$. In this paper, structural properties of $B_1(G)$ and its complement including traversability and eccentricity properties are studied. In addition, solutions for Boolean function graphs that are total graphs, quasi-total graphs and middle graphs are obtained.},
author = {Janakiraman, T. N., Muthammai, S., Bhanumathi, M.},
journal = {Mathematica Bohemica},
keywords = {eccentricity; self-centered graph; middle graph; Boolean function graph; eccentricity; self-centered graph; middle graph},
language = {eng},
number = {2},
pages = {113-134},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the Boolean function graph of a graph and on its complement},
url = {http://eudml.org/doc/249575},
volume = {130},
year = {2005},
}

TY - JOUR
AU - Janakiraman, T. N.
AU - Muthammai, S.
AU - Bhanumathi, M.
TI - On the Boolean function graph of a graph and on its complement
JO - Mathematica Bohemica
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 130
IS - 2
SP - 113
EP - 134
AB - 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 $B(G,L(G),\mathop {\mathrm {N}INC})$ of $G$ is a graph with vertex set $V(G)\cup E(G)$ and two vertices in $B(G,L(G),\mathop {\mathrm {N}INC})$ 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 $G$. For brevity, this graph is denoted by $B_1(G)$. In this paper, structural properties of $B_1(G)$ and its complement including traversability and eccentricity properties are studied. In addition, solutions for Boolean function graphs that are total graphs, quasi-total graphs and middle graphs are obtained.
LA - eng
KW - eccentricity; self-centered graph; middle graph; Boolean function graph; eccentricity; self-centered graph; middle graph
UR - http://eudml.org/doc/249575
ER -

References

top
  1. On characterizations of the middle graphs, TRU Math. 11 (1975), 35–39. (1975) MR0414436
  2. 10.1017/S0305004100041657, Proc. Camb. Philos. Soc. 63 (1967), 679–681. (1967) Zbl0158.20703MR0211896DOI10.1017/S0305004100041657
  3. Graph Theory with Application, Macmillan, London, 1976. (1976) 
  4. Semi-total graphs II, Graph Theory Research Report, Karnatak University 2 (1973), 5–9. (1973) 
  5. 10.1016/0012-365X(76)90037-6, Discrete Math. 14 (1976), 247–256. (1976) MR0414435DOI10.1016/0012-365X(76)90037-6
  6. Graph Theory, Addison-Wesley, Reading, Mass., 1969. (1969) Zbl0196.27202MR0256911
  7. The neighborhood number of a graph, Indian J. Pure Appl. Math. 16 (1985), 126–132. (1985) MR0780299
  8. 10.1016/0012-365X(84)90137-7, Discrete Math. 48 (1984), 113–119. (1984) MR0732207DOI10.1016/0012-365X(84)90137-7
  9. 10.2307/2371086, Am. J. Math. 54 (1932), 150–168. (1932) Zbl0003.32804MR1506881DOI10.2307/2371086

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.