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About Pendent Inclusive Sets In Graphs
D.K.Thakkar 1 , N.J.Savaliya 2
Section:Research Paper, Product Type: Isroset-Journal
Vol.6 ,
Issue.3 , pp.128-135, Jun-2019
CrossRef-DOI: https://doi.org/10.26438/ijsrmss/v6i3.128135
Online published on Jun 30, 2019
Copyright © D.K.Thakkar , N.J.Savaliya . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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IEEE Style Citation: D.K.Thakkar , N.J.Savaliya, “About Pendent Inclusive Sets In Graphs,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.3, pp.128-135, 2019.
MLA Style Citation: D.K.Thakkar , N.J.Savaliya "About Pendent Inclusive Sets In Graphs." International Journal of Scientific Research in Mathematical and Statistical Sciences 6.3 (2019): 128-135.
APA Style Citation: D.K.Thakkar , N.J.Savaliya, (2019). About Pendent Inclusive Sets In Graphs. International Journal of Scientific Research in Mathematical and Statistical Sciences, 6(3), 128-135.
BibTex Style Citation:
@article{_2019,
author = {D.K.Thakkar , N.J.Savaliya},
title = {About Pendent Inclusive Sets In Graphs},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {6 2019},
volume = {6},
Issue = {3},
month = {6},
year = {2019},
issn = {2347-2693},
pages = {128-135},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=1336},
doi = {https://doi.org/10.26438/ijcse/v6i3.128135}
publisher = {IJCSE, Indore, INDIA},
}
RIS Style Citation:
TY - JOUR
DO = {https://doi.org/10.26438/ijcse/v6i3.128135}
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=1336
TI - About Pendent Inclusive Sets In Graphs
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - D.K.Thakkar , N.J.Savaliya
PY - 2019
DA - 2019/06/30
PB - IJCSE, Indore, INDIA
SP - 128-135
IS - 3
VL - 6
SN - 2347-2693
ER -
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Abstract :
We introduce a new concept called pendent inclusive set in graphs. We also define maximum and 1-maximal pendent inclusive sets in graphs. We prove that for a graph G having a pendent vertex V(G) is the only maximum and 1-maximum pendent inclusive set of a graph. We prove a characterization of a 1-maximal pendent inclusive set of a graph can have at most ∆(G) pendent vertices. We also prove that if u and v have same degree. We further, prove that for any k_regular graph with K≥1, all 1-maximal pendent inclusive set have the same cardinality N-k+1. We also prove several results related to the effect of vertex removal and edge removal on pendent inclusive number of a graph.
Key-Words / Index Term :
pendent inclusive set, maximum pendent inclusive set, maximal pendent inclusive set, k- dominating set, pendent edge, isolated edge
References :
[1] D.K.Thakkar and N.J.Savaliya, “About Isolate Inclusive sets in Graphs “, International Journal of Mathematical And its Applications, Vol. 6, Issue 2-B, pp. 361-367, 2018.
[2] D.K.Thakkar and N.J.Savaliya, “On Isolate Inclusive sets in Graphs “, International Journal of Innovation in Science and Mathematics, Vol. 5, Issue 3, pp. 74-76, 2017.
[3] T.W.Haynes, S.T.Hedetniemi, P.J.Slater, “Fundamental of Domination In graphs”, Marcel Dekker, New York, 1998.
[4] T.W.Haynes, S.T.Hedetniemi, P.J.Slater, “Domination In Graphs Advanced Topics”, Marcel Dekker, New York, 1998.
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