Commutativity of Some Graph Operators
DOI:
https://doi.org/10.37591/rrdms.v6i1.1939Keywords:
Line graph, Graph Operators, CommutativityAbstract
Abstract
The line graph L(G) of a graph G has the edges of G as its vertices and two distinct edges of G are adjacent in L(G) if they are incident in G. In this paper we consider the commutativity of the line graph operator with some other operators such as Gallai graph Γ(G), anti- Gallai graph Δ(G), kth power of a graph Powk(G), k-distance graph Tk(G), cycle graph Cy(G), block graph B(G), subdivision graph S(G), total graph T(G) and middle graph Mid(G).
Keywords: Line graph, graph operators, commutativity
Cite this Article
Jeepamol J. Palathingal, Aparna Lakshmanan S. Commutativity of Some Graph Operators. Research & Reviews: Discrete Mathematical Structures. 2019; 6(1): 1–5p.
References
E. L. Tan, Some notes on cycle graphs, Discrete math. 105(1992)221-226cited in sect. 15.6.
E. Prisner, Graph Dynamics, Longman (1995).
F. Harary, Graph Theory, Narora publishing House, 1988.
F. Harary, C. Hoede. D. Kadlacek, Graph-valued functions related to step graphs, J.comb. Inf. Syst. Sci. 7 (1982) 231- 246 (Zbl.532.05010) cited in sect 16.3,16.4.
F. Joos, V. B. Le, D. Rautenbach, Forest and trees in Gallai graphs, Discrete Math., 338(2) (2015), 190 - 195.
Jeepamol J Palathingal and Aparna Lakshmanan S, Gallai and anti-Gallai Graph Operators (accepted in ENDM)
K. Pravas and A. Vijayakumar, The median problem on symmetric bipartite graphs, proceedings of the International Conference on Theoretical Computer
Science and Discrete Mathematics 2016, Kalasalingam University: ICTCSDM 2016, LNCS 10398, pp. 262-270, 2017.
R. Balakrishnan, K. Ranganathan, A text book of graph theory, Springer (1999).
R. Motwani, M. Sudan, Computing roots of graphs is hard, Discrete Appl. Math. 54 (1994) 81-88 sect 14.3,16.2.
V. B. Le, Gallai graphs and anti-Gallai graphs, Discrete Math., 159 (1996), 179 - 189.
V. B. Le, Mortality of iterated Gallai graphs, Period. Math. Hungar., 27(2) (1993), 105 - 124.
Y. Egawa, M. Kano, E. L. Tan, On cycle graphs, Ars Conbinatoria 32 (1991) 97-113 (Zbl.755.05066) cited in sect. 11.2, 15.6.
Y.L. Lin, S. S. Skiena, Algorithm for square root of graphs, SIAM J. Discrete Math. 8 (1995) 99-118. sect 16.2, 17.5.
Downloads
Published
Issue
Section
License
Declaration and Copyright Transfer Form
(to be completed by authors)
I/ We, the undersigned author(s) of the submitted manuscript, hereby declare, that the above manuscript which is submitted for publication in the STM Journals(s), is not published already in part or whole (except in the form of abstract) in any journal or magazine for private or public circulation, and, is not under consideration of publication elsewhere.
- I/We will not withdraw the manuscript after 1 week of submission as I have read the Author Guidelines and will adhere to the guidelines.
- I/We Author(s ) have niether given nor will give this manuscript elsewhere for publishing after submitting in STM Journal(s).
- I/ We have read the original version of the manuscript and am/ are responsible for the thought contents embodied in it. The work dealt in the manuscript is my/ our own, and my/ our individual contribution to this work is significant enough to qualify for authorship.
- I/We also agree to the authorship of the article in the following order:
Author’s name
1. ________________
2. ________________
3. ________________
4. ________________
| We Author(s) tick this box and would request you to consider it as our signature as we agree to the terms of this Copyright Notice, which will apply to this submission if and when it is published by this journal. |
