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On Connected 2-K n -Residual Graphs

Content Provider	Springer Nature Link
Author	Liao, Jiangdong Yang, Shihui Deng, Yong
Copyright Year	2012
Abstract	A graph G is said to be K n -residual if for every point u in G, the graph obtained by removing the closed neighborhood of u from G is isomorphic to K n . We inductively define a multiply-K n -residual graph by saying that G is m-K n -residual if the removal of the closed neighborhood of any vertex of G results in an (m – 1)-K n -residual graphs. Erdös, Harary and Klawe [2] determined the minimum order of the m−K n -residual graphs for all m and n, which are not necessarily connected, the minimum order of connected; K n -residual graphs, all K n -residual extremal graphs. They also stated some conjectures regarding the connected case. In this paper, we determine the minimum order of a connected 2-K n -residual graph and specify the extremal graphs, expect for n = 3. In particular, we determining only one connected 2-K 4-residual graph of minimal order, and show that there is a connected 2-K 6-residual graph non isomorphic to K 8 × K 3 with minimum order. Finally we present and a revised version of the conjecture in [2].
Ending Page	641
Page Count	17
Starting Page	625
File Format	PDF
ISSN	16605446
e-ISSN	16605454
Journal	Mediterranean Journal of Mathematics
Issue Number	2
Volume Number	10
Language	English
Publisher	SP Birkhäuser Verlag Basel
Publisher Date	2012-10-11
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) Structural characterization of families of graphs Extremal problems Mathematics composite graph Residual-graph Cartesian product
Content Type	Text
Resource Type	Article
Subject	Mathematics

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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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Embedding complete multi-partite graphs into Cartesian product of paths and cycles

Chromatic uniqueness of certain complete tripartite graphs

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On Connected 2-K n -Residual Graphs

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On Connected 2-K n -Residual Graphs