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1

Kujur, Chiranjilal. "Proper d-Lucky Number for Certain Rooted Product Graphs." Indian Journal Of Science And Technology 16, no. 4 (2023): 249–53. http://dx.doi.org/10.17485/ijst/v16i4.2146.

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2

vathi, S. Kala, and K. Pal ani. "(G,D)-Bondage and (G,D)-Nonbondage Number of a Graph." International Journal of Mathematics Trends and Technology 57, no. 1 (2018): 67–72. http://dx.doi.org/10.14445/22315373/ijmtt-v57p510.

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3

de Jong, Theo. "The virtual number of D∞ points I." Topology 29, no. 2 (1990): 175–84. http://dx.doi.org/10.1016/0040-9383(90)90006-6.

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4

de Jong, Johan, and Theo de Jong. "The virtual number of D∞ points II." Topology 29, no. 2 (1990): 185–88. http://dx.doi.org/10.1016/0040-9383(90)90007-7.

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5

Cohn, J. H. E. "On the number of D-optimal designs." Journal of Combinatorial Theory, Series A 66, no. 2 (1994): 214–25. http://dx.doi.org/10.1016/0097-3165(94)90063-9.

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6

Dong, Hai-Rong, Feng Feng, and Hai-Bo Li. "Lepton number violation in D meson decay." Chinese Physics C 39, no. 1 (2015): 013101. http://dx.doi.org/10.1088/1674-1137/39/1/013101.

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7

A, Prasanna, та Mohamedazarudeen N. "Connected 𝐷 - Eccentric Domination in Graphs". Indian Journal of Science and Technology 17, № 36 (2024): 3776–80. https://doi.org/10.17485/IJST/v17i36.2672.

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Abstract <strong>Objectives:</strong>&nbsp;To introduce connected -eccentric point set, connected -eccentric number, connected -eccentric dominating set, connected -eccentric domination number in a graph and related concepts.&nbsp;<strong>Methods:</strong>&nbsp;-distance in graphs are used to find the connected -eccentric number and connected -eccentric domination number in graphs.&nbsp;<strong>Findings:</strong>&nbsp;The new term connected -eccentric domination in graphs are used in varies field like to construct least number of cell phone tower in low cost and traffic signal also.&nbsp;<stro
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8

Chiranjilal, Kujur. "Proper d-Lucky Number for Certain Rooted Product Graphs." Indian Journal of Science and Technology 16, no. 4 (2023): 249–53. https://doi.org/10.17485/IJST/v16i4.2146.

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ABSTRACT <strong>Objectives:</strong>&nbsp;In this study, rooted product of path with cycle, path with complete graph cycle with complete graph and complete graph with complete graphs are taken and examined for the existence of d-lucky labeling for the same.<strong>&nbsp;Methods:</strong>&nbsp;The rooted product graphs are obtained of path with cycle, path with complete graph, cycle with complete graph and complete graph with itself and then proper d-lucky numbers are obtained for the above mentioned graphs. Construction and descriptive method are used to prove the results.&nbsp;<strong>Findin
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9

BEHRISCH, MICHAEL, AMIN COJA-OGHLAN, and MIHYUN KANG. "The Asymptotic Number of Connected d-Uniform Hypergraphs." Combinatorics, Probability and Computing 23, no. 3 (2014): 367–85. http://dx.doi.org/10.1017/s0963548314000029.

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For d ≥ 2, let Hd(n,p) denote a random d-uniform hypergraph with n vertices in which each of the $\binom{n}{d}$ possible edges is present with probability p=p(n) independently, and let Hd(n,m) denote a uniformly distributed d-uniform hypergraph with n vertices and m edges. Let either H=Hd(n,m) or H=Hd(n,p), where m/n and $\binom{n-1}{d-1}p$ need to be bounded away from (d−1)−1 and 0 respectively. We determine the asymptotic probability that H is connected. This yields the asymptotic number of connected d-uniform hypergraphs with given numbers of vertices and edges. We also derive a local limit
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10

John, J., P. Arul Paul Sudhahar, and D. Stalin. "On the (M, D) number of a graph." Proyecciones (Antofagasta) 38, no. 2 (2019): 255–66. http://dx.doi.org/10.4067/s0716-09172019000200255.

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11

Teichert, Hanns-Martin. "The sum number of d-partite complete hypergraphs." Discussiones Mathematicae Graph Theory 19, no. 1 (1999): 79. http://dx.doi.org/10.7151/dmgt.1087.

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12

Berndt, Bruce C. "Exercises in Number Theory. By D. P. Parent." American Mathematical Monthly 93, no. 8 (1986): 667–68. http://dx.doi.org/10.1080/00029890.1986.11971919.

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13

Ackerman, Eyal, Gill Barequet, Ron Y. Pinter, and Dan Romik. "The number of guillotine partitions in d dimensions." Information Processing Letters 98, no. 4 (2006): 162–67. http://dx.doi.org/10.1016/j.ipl.2006.01.011.

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14

John, J., P. Arul Paul Sudhahar, and D. Stalin. "On the (M,D) number of a graph." Proyecciones (Antofagasta) 38, no. 2 (2019): 255–66. https://doi.org/10.22199/issn.0717-6279-3570.

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For a connected graph G = (V, E), a monophonic set of G is a set M ⊆ V (G) such that every vertex of G is contained in a monophonic path joining some pair of vertices in M. A subset D of vertices in G is called dominating set if every vertex not in D has at least one neighbour in D. A monophonic dominating set M is both a monophonic and a dominating set. The monophonic, dominating, monophonic domination number m(G), γ(G), γm(G) respectively are the minimum cardinality of the respective sets in G. Monophonic domination number of certain classes of graphs are determined. Connected graph of order
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15

Prałat, Paweł, and Harjas Singh. "Hopping forcing number in random d-regular graphs." Discrete Mathematics 348, no. 12 (2025): 114644. https://doi.org/10.1016/j.disc.2025.114644.

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16

Boussakta, S., O. Alshibami, M. Aziz, and A. G. J. Holt. "3-D vector radix algorithm for the 3-D new Mersenne number transform." IEE Proceedings - Vision, Image, and Signal Processing 148, no. 2 (2001): 115. http://dx.doi.org/10.1049/ip-vis:20010312.

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17

Jukić Matić, Ljerka. "On D(w)-quadruples in the rings of integers of certain pure number fields." Glasnik Matematicki 49, no. 1 (2014): 37–46. http://dx.doi.org/10.3336/gm.49.1.04.

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18

Bréhamet, Lionel. "Egyptian 2/D Table (D Composite Number): Continuation and End of a Consistent Project." History Research 5, no. 3 (2017): 16. http://dx.doi.org/10.11648/j.history.20170503.11.

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19

Alcántara, Claudia R. "Foliations on $$\mathbb {CP}^2$$ CP 2 of degree d with a singular point with Milnor number $$d^2+d+1$$ d 2 + d + 1." Revista Matemática Complutense 31, no. 1 (2017): 187–99. http://dx.doi.org/10.1007/s13163-017-0239-0.

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20

K. John Bosco et al.,, K. John Bosco et al ,. "On Radio Square Sum D-Distance Number of Graphs." International Journal of Mathematics and Computer Applications Research 11, no. 1 (2021): —29–36. http://dx.doi.org/10.24247/ijmcarjun20213.

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21

Thomson, Neil R., Craig J. Rodger, and Mark A. Clilverd. "Tropical daytime lower D-region dependence on sunspot number." Journal of Geophysical Research: Space Physics 117, A10 (2012): n/a. http://dx.doi.org/10.1029/2012ja018077.

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22

ROBERTS, ALAN, and ANTONIOS SYMVONIS. "ON THE ROUTING NUMBER OF COMPLETE d-ARY TREES." International Journal of Foundations of Computer Science 12, no. 04 (2001): 411–34. http://dx.doi.org/10.1142/s0129054101000564.

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We consider the routing number of trees, denoted by rt(), with respect to the matching routing model. For an arbitrary n-node tree T, it is known that rt(T) &lt; 3n/2 + O( log n). In this paper, by providing a recursive off-line permutation routing algorithm, we show that the routing number of an n-node complete d-ary tree of height h(T) &gt; 1 is bounded from above by n + o(n). This is near optimal since, for an n-node complete d-ary tree T of height h(T) &gt; 1 it holds that rt(T) ≥ n.
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23

Nicholas, T., and K. John Bosco. "Radio mean D-distance number of cycle-related graphs." International Journal of Mathematics Trends and Technology 40, no. 3 (2016): 247–51. http://dx.doi.org/10.14445/22315373/ijmtt-v40p530.

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24

Kemkes, Graeme, Xavier Pérez-Giménez, and Nicholas Wormald. "On the chromatic number of random d-regular graphs." Advances in Mathematics 223, no. 1 (2010): 300–328. http://dx.doi.org/10.1016/j.aim.2009.08.006.

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25

BEHRISCH, MICHAEL, AMIN COJA-OGHLAN, and MIHYUN KANG. "‘The Asymptotic Number of Connected d-Uniform Hypergraphs’ — CORRIGENDUM." Combinatorics, Probability and Computing 24, no. 1 (2014): 373–75. http://dx.doi.org/10.1017/s0963548314000698.

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26

Lee, Jae-Ho, and Dae-Kwang Kim. "Association between Mitochondrial D-loop Polymorphism and Copy Number." Korean Journal of Physical Anthropology 27, no. 3 (2014): 131. http://dx.doi.org/10.11637/kjpa.2014.27.3.131.

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27

AZIZOĞLU, M. CEMIL, and ÖMER EĞECIOĞLU. "THE ISOPERIMETRIC NUMBER OF d–DIMENSIONAL k–ARY ARRAYS." International Journal of Foundations of Computer Science 10, no. 03 (1999): 289–300. http://dx.doi.org/10.1142/s0129054199000216.

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The d–dimensional k-ary array [Formula: see text] is the d–fold Cartesian product graph of the path graph Pk with k vertices. We show that the (edge) isoperimetric number [Formula: see text] of [Formula: see text] is given by [Formula: see text] and identify the cardinalities and the structure of the isoperimetric sets. For odd k, the cardinalities of isoperimetric sets in [Formula: see text] are [Formula: see text], whereas every isoperimetric set for k even has cardinality [Formula: see text].
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28

FAST, STEPHEN H. "The Cardinal Number d and Convergent Sequences in Q." Annals of the New York Academy of Sciences 704, no. 1 Papers on Gen (1993): 126–28. http://dx.doi.org/10.1111/j.1749-6632.1993.tb52514.x.

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29

Kohl, Anja. "The L(d,1)-number of powers of paths." Discrete Mathematics 309, no. 10 (2009): 3427–30. http://dx.doi.org/10.1016/j.disc.2008.08.018.

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30

Walker, Michael W., Lejun Shao, and Richard A. Volz. "Estimating 3-D location parameters using dual number quaternions." CVGIP: Image Understanding 54, no. 3 (1991): 358–67. http://dx.doi.org/10.1016/1049-9660(91)90036-o.

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31

Liu, Xizhi. "d-cluster-free sets with a given matching number." European Journal of Combinatorics 82 (December 2019): 103000. http://dx.doi.org/10.1016/j.ejc.2019.103000.

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32

Martinez-Sebastian, M.J., and J.L. Mensua. "Abdominal bristle number and sex-dimorphism in D. subobscura." Drosophila Information Service 61 (June 5, 1985): 116. https://doi.org/10.5281/zenodo.10757389.

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33

Poomalai, P., R. Vikramaprasad, and P. Malliga. "ON RADIO ANALYTIC MEAN D-DISTANCE NUMBER OF MORE GRAPHS." Advances in Mathematics: Scientific Journal 9, no. 11 (2020): 9237–45. http://dx.doi.org/10.37418/amsj.9.11.29.

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A Radio Analytic Mean D-distance labeling of associated diagram $G$ is a balanced guide $v$ from the vertex set $V(G)$ to $N$ such that for two distinct vertices $u$ and $v$ of $G$. $d^D\left(u,v\right) +\left\lceil \frac{\left|f({u)}^2-f(v)^2\right|}{2}\right\rceil \ge 1+\ {diam}^{D\ }(G)$.
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34

Gaál, István, and Michael E. Pohst. "On calculating the number N(D) of global cubic fields F of given discriminant D." Journal of Number Theory 236 (July 2022): 479–91. http://dx.doi.org/10.1016/j.jnt.2021.08.017.

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35

Zhang, Xinhong, Caijuan Xue, and Ruijuan Li. "The domination number of round digraphs." Open Mathematics 18, no. 1 (2020): 1625–34. http://dx.doi.org/10.1515/math-2020-0084.

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Abstract The concept of the domination number plays an important role in both theory and applications of digraphs. Let D = ( V , A ) D=(V,A) be a digraph. A vertex subset T ⊆ V ( D ) T\subseteq V(D) is called a dominating set of D, if there is a vertex t ∈ T t\in T such that t v ∈ A ( D ) tv\in A(D) for every vertex v ∈ V ( D ) \ T v\in V(D)\backslash T . The dominating number of D is the cardinality of a smallest dominating set of D, denoted by γ ( D ) \gamma (D) . In this paper, the domination number of round digraphs is characterized completely.
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36

Ahmed, Chwas, Paul Martin, and Volodymyr Mazorchuk. "On the number of principal ideals in d-tonal partition monoids." Annals of Combinatorics 25, no. 1 (2021): 79–113. http://dx.doi.org/10.1007/s00026-020-00518-z.

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AbstractFor a positive integer d, a non-negative integer n and a non-negative integer $$h\le n$$ h ≤ n , we study the number $$C_{n}^{(d)}$$ C n ( d ) of principal ideals; and the number $$C_{n,h}^{(d)}$$ C n , h ( d ) of principal ideals generated by an element of rank h, in the d-tonal partition monoid on n elements. We compute closed forms for the first family, as partial cumulative sums of known sequences. The second gives an infinite family of new integral sequences. We discuss their connections to certain integral lattices as well as to combinatorics of partitions.
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37

Chen, Xiaohong, and Baoyindureng Wu. "Feedback Arc Number and Feedback Vertex Number of Cartesian Product of Directed Cycles." Discrete Dynamics in Nature and Society 2019 (December 16, 2019): 1–4. http://dx.doi.org/10.1155/2019/7028573.

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For a digraph D, the feedback vertex number τD, (resp. the feedback arc number τ′D) is the minimum number of vertices, (resp. arcs) whose removal leaves the resultant digraph free of directed cycles. In this note, we determine τD and τ′D for the Cartesian product of directed cycles D=Cn1→□Cn2→□…Cnk→. Actually, it is shown that τ′D=n1n2…nk∑i=1k1/ni, and if nk≥…≥n1≥3 then τD=n2…nk.
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38

Safeer P. A., Sadiquali A., Santhoshkumar K. R. "The Split (D, C) Number of a Graph and Related Properties." Tuijin Jishu/Journal of Propulsion Technology 44, no. 4 (2023): 7202–9. http://dx.doi.org/10.52783/tjjpt.v44.i4.2555.

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In this paper, we introduce the concept of dominating chromatic set [(D, C)-set in short] and split dominating chromatic set of a connected graph G, it leads to an associated color variable, namely (D, C) number and split (D, C) number of G. It characterizes the parameter, along with optimized dominating sets. Also, the split (D, C) number of some standard graphs are identified.
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39

Nugroho, E., and K. A. Sugeng. "On d-local strong rainbow connection number of prism graphs." Journal of Physics: Conference Series 1722 (January 2021): 012053. http://dx.doi.org/10.1088/1742-6596/1722/1/012053.

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40

QU, Jianwu, Yuichi MURAI, and Fujio YAMAMOTO. "A213 Reynolds Number Dependency of 3-D Bubble-Bubble Interaction." Journal of the Visualization Society of Japan 23, Supplement1 (2003): 247–50. http://dx.doi.org/10.3154/jvs.23.supplement1_247.

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41

SUNDARAMOORTHY, RAJKUMAR, and NALLIAH MOVIRI CHETTIAR. "On $(a,d)$-edge local antimagic coloring number of graphs." Turkish Journal of Mathematics 46, no. 5 (2022): 1994–2002. http://dx.doi.org/10.55730/1300-0098.3247.

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42

Fujita, Kazuhisa. "Estimation of the number of clusters on d-dimensional sphere." Artificial Intelligence Research 10, no. 1 (2021): 57. http://dx.doi.org/10.5430/air.v10n1p57.

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Spherical data is distributed on the sphere. The data appears in various fields such as meteorology, biology, and natural language processing. However, a method for analysis of spherical data does not develop enough yet. One of the important issues is an estimation of the number of clusters in spherical data. To address the issue, I propose a new method called the Spherical X-means (SX-means) that can estimate the number of clusters on d-dimensional sphere. The SX-means is the model-based method assuming that the data is generated from a mixture of von Mises-Fisher distributions. The present p
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43

Nugroho, E., and K. A. Sugeng. "On d-local strong rainbow connection number of prism graphs." Journal of Physics: Conference Series 1722 (January 2021): 012053. http://dx.doi.org/10.1088/1742-6596/1722/1/012053.

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44

Alshibami, O., S. Boussakta, and M. Aziz. "Fast algorithm for the 2-D new Mersenne number transform." Signal Processing 81, no. 8 (2001): 1725–35. http://dx.doi.org/10.1016/s0165-1684(01)00068-8.

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45

KAKUDA, K., N. TOSAKA, and T. NAKAMURA. "Finite Element Analysis for 3-D High Reynolds Number Flows." International Journal of Computational Fluid Dynamics 7, no. 1-2 (1996): 163–78. http://dx.doi.org/10.1080/10618569608940759.

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46

Dreyssé, H., A. Mokrani, S. Bouarab, and C. Demangeat. "Magnetism and coordination number for systems with unfilled d shells." Surface Science Letters 251-252 (July 1991): A308. http://dx.doi.org/10.1016/0167-2584(91)90823-a.

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47

Majumder, Catherine A. Hier, David A. Yuen, Erik O. Sevre, John M. Boggs, and Stephen Y. Bergeron. "Finite Prandtl number 2-D convection at high Rayleigh numbers." Visual Geosciences 7, no. 1 (2002): 1–53. http://dx.doi.org/10.1007/s10069-002-0004-4.

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48

Charpentier, C., and É. Sopena. "The incidence game chromatic number of (a,d)-decomposable graphs." Journal of Discrete Algorithms 31 (March 2015): 14–25. http://dx.doi.org/10.1016/j.jda.2014.10.001.

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49

Benaissa, M., S. S. Dlay, and A. G. J. Holt. "VLSI implementation issues for the 2-D Fermat number transform." Signal Processing 23, no. 3 (1991): 257–72. http://dx.doi.org/10.1016/0165-1684(91)90004-3.

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50

Dreyssé, H., A. Mokrani, S. Bouarab, and C. Demangeat. "Magnetism and coordination number for systems with unfilled d shells." Surface Science 251-252 (July 1991): 41–45. http://dx.doi.org/10.1016/0039-6028(91)90950-w.

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