Graphical virtual links and a polynomial for signed cyclic graphs

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Graphical virtual links and a polynomial for signed cyclic graphs. / Deng, Qingying; Jin, Xian'An; Kauffman, Louis H.

In: Journal of Knot Theory and its Ramifications, Vol. 27, No. 10, 1850054, 01.09.2018.

Research output: Contribution to journal › Article › peer-review

Harvard

Deng, Q, Jin, XA & Kauffman, LH 2018, 'Graphical virtual links and a polynomial for signed cyclic graphs', Journal of Knot Theory and its Ramifications, vol. 27, no. 10, 1850054. https://doi.org/10.1142/S0218216518500542

APA

Deng, Q., Jin, XA., & Kauffman, L. H. (2018). Graphical virtual links and a polynomial for signed cyclic graphs. Journal of Knot Theory and its Ramifications, 27(10), [1850054]. https://doi.org/10.1142/S0218216518500542

Vancouver

Deng Q, Jin XA, Kauffman LH. Graphical virtual links and a polynomial for signed cyclic graphs. Journal of Knot Theory and its Ramifications. 2018 Sept 1;27(10):1850054. doi: 10.1142/S0218216518500542

Author

Deng, Qingying ; Jin, Xian'An ; Kauffman, Louis H. / Graphical virtual links and a polynomial for signed cyclic graphs. In: Journal of Knot Theory and its Ramifications. 2018 ; Vol. 27, No. 10.

BibTeX

@article{dc191deed2b54572899b8817078cfd84,

title = "Graphical virtual links and a polynomial for signed cyclic graphs",

abstract = "For a signed cyclic graph G, we can construct a unique virtual link L by taking the medial construction and converting 4-valent vertices of the medial graph to crossings according to the signs. If a virtual link can occur in this way then we say that the virtual link is graphical. In this paper, we shall prove that a virtual link L is graphical if and only if it is checkerboard colorable. On the other hand, we introduce a polynomial F[G] for signed cyclic graphs, which is defined via a deletion-marking recursion. We shall establish the relationship between F[G] of a signed cyclic graph G and the bracket polynomial of one of the virtual link diagrams associated with G. Finally, we give a spanning subgraph expansion for F[G].",

keywords = "bracket polynomial, checkerboard colorable, F [ G ] polynomial, graphical, orientable ribbon graphs, signed cyclic graph, Virtual link, F[G] polynomial, KNOTS, SURFACES",

author = "Qingying Deng and Xian'An Jin and Kauffman, {Louis H.}",

note = "Publisher Copyright: {\textcopyright} 2018 World Scientific Publishing Company.",

year = "2018",

month = sep,

day = "1",

doi = "10.1142/S0218216518500542",

language = "English",

volume = "27",

journal = "Journal of Knot Theory and its Ramifications",

issn = "0218-2165",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "10",

}

RIS

TY - JOUR

T1 - Graphical virtual links and a polynomial for signed cyclic graphs

AU - Deng, Qingying

AU - Jin, Xian'An

AU - Kauffman, Louis H.

PY - 2018/9/1

Y1 - 2018/9/1

N2 - For a signed cyclic graph G, we can construct a unique virtual link L by taking the medial construction and converting 4-valent vertices of the medial graph to crossings according to the signs. If a virtual link can occur in this way then we say that the virtual link is graphical. In this paper, we shall prove that a virtual link L is graphical if and only if it is checkerboard colorable. On the other hand, we introduce a polynomial F[G] for signed cyclic graphs, which is defined via a deletion-marking recursion. We shall establish the relationship between F[G] of a signed cyclic graph G and the bracket polynomial of one of the virtual link diagrams associated with G. Finally, we give a spanning subgraph expansion for F[G].

AB - For a signed cyclic graph G, we can construct a unique virtual link L by taking the medial construction and converting 4-valent vertices of the medial graph to crossings according to the signs. If a virtual link can occur in this way then we say that the virtual link is graphical. In this paper, we shall prove that a virtual link L is graphical if and only if it is checkerboard colorable. On the other hand, we introduce a polynomial F[G] for signed cyclic graphs, which is defined via a deletion-marking recursion. We shall establish the relationship between F[G] of a signed cyclic graph G and the bracket polynomial of one of the virtual link diagrams associated with G. Finally, we give a spanning subgraph expansion for F[G].

KW - bracket polynomial

KW - checkerboard colorable

KW - F [ G ] polynomial

KW - graphical

KW - orientable ribbon graphs

KW - signed cyclic graph

KW - Virtual link

KW - F[G] polynomial

KW - KNOTS

KW - SURFACES

UR - http://www.scopus.com/inward/record.url?scp=85052681216&partnerID=8YFLogxK

U2 - 10.1142/S0218216518500542

DO - 10.1142/S0218216518500542

M3 - Article

AN - SCOPUS:85052681216

VL - 27

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

SN - 0218-2165

IS - 10

M1 - 1850054

ER -

ID: 16336580