| Title:
|
On the Boolean function graph of a graph and on its complement (English) |
| Author:
|
Janakiraman, T. N. |
| Author:
|
Muthammai, S. |
| Author:
|
Bhanumathi, M. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
130 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
113-134 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $G$. 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. (English) |
| Keyword:
|
eccentricity |
| Keyword:
|
self-centered graph |
| Keyword:
|
middle graph |
| Keyword:
|
Boolean function graph |
| MSC:
|
05C12 |
| MSC:
|
05C15 |
| MSC:
|
05C45 |
| MSC:
|
05C75 |
| MSC:
|
06E30 |
| idZBL:
|
Zbl 1110.05086 |
| idMR:
|
MR2148646 |
| DOI:
|
10.21136/MB.2005.134130 |
| . |
| Date available:
|
2009-09-24T22:19:10Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134130 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[5] T. Hamada, I. Yoshimura: Traversability and connectivity of the middle graph of a graph.Discrete Math. 14 (1976), 247–256. MR 0414435, 10.1016/0012-365X(76)90037-6 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| . |
