On the intersection power graph of a finite group
Given a group G, the intersection power graph of G, denoted by GI(G), is the graph with vertex set G and two distinct vertices x and y are adjacent in GI(G) if there exists a non-identity element z ∈ G such that xm=z=yn, for some m, n ∈ N, i.e. x ∼ y in GI(G) if ⟨x⟩ ∩ ⟨y⟩ ≠ {e} and e is adjacent to...
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| Format: | EJournal Article |
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GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB,
2018-04-03.
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| LEADER | 01960 am a22002413u 4500 | ||
|---|---|---|---|
| 001 | EJGTA_465_pdf_73 | ||
| 042 | |a dc | ||
| 100 | 1 | 0 | |a Bera, Sudip; Department of Mathematics, Visva-Bharati, Santin |e author |
| 100 | 1 | 0 | |a UGC, INDIA |e contributor |
| 245 | 0 | 0 | |a On the intersection power graph of a finite group |
| 260 | |b GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, |c 2018-04-03. | ||
| 500 | |a https://www.ejgta.org/index.php/ejgta/article/view/465 | ||
| 520 | |a Given a group G, the intersection power graph of G, denoted by GI(G), is the graph with vertex set G and two distinct vertices x and y are adjacent in GI(G) if there exists a non-identity element z ∈ G such that xm=z=yn, for some m, n ∈ N, i.e. x ∼ y in GI(G) if ⟨x⟩ ∩ ⟨y⟩ ≠ {e} and e is adjacent to all other vertices, where e is the identity element of the group G. Here we show that the graph GI(G) is complete if and only if either G is cyclic p-group or G is a generalized quaternion group. Furthermore, GI(G) is Eulerian if and only if ∣G∣ is odd. We characterize all abelian groups and also all non-abelian p-groups G, for which GI(G) is dominatable. Beside, we determine the automorphism group of the graph GI(Zn), when n ≠ pm. | ||
| 540 | |a Copyright (c) 2018 Electronic Journal of Graph Theory and Applications (EJGTA) | ||
| 546 | |a eng | ||
| 690 | |a automorphism group, intersection power graph, planar, p-groups | ||
| 655 | 7 | |a info:eu-repo/semantics/article |2 local | |
| 655 | 7 | |a info:eu-repo/semantics/publishedVersion |2 local | |
| 655 | 7 | |a Peer-reviewed Article |2 local | |
| 786 | 0 | |n Electronic Journal of Graph Theory and Applications (EJGTA); Vol 6, No 1 (2018): Electronic Journal of Graph Theory and Applications; 178-189 | |
| 786 | 0 | |n 2338-2287 | |
| 787 | 0 | |n https://www.ejgta.org/index.php/ejgta/article/view/465/pdf_73 | |
| 856 | 4 | 1 | |u https://www.ejgta.org/index.php/ejgta/article/view/465/pdf_73 |z Get Fulltext |