Academic literature on the topic 'Rainbow Connection'

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Journal articles on the topic "Rainbow Connection"

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Chartrand, Gary, Garry L. Johns, Kathleen A. McKeon, and Ping Zhang. "Rainbow connection in graphs." Mathematica Bohemica 133, no. 1 (2008): 85–98. http://dx.doi.org/10.21136/mb.2008.133947.

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Bustan, A. W., A. N. M. Salman, and P. E. Putri. "On the locating rainbow connection number of amalgamation of complete graphs." Journal of Physics: Conference Series 2543, no. 1 (July 1, 2023): 012004. http://dx.doi.org/10.1088/1742-6596/2543/1/012004.

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Abstract Locating rainbow connection number determines the minimum number of colors connecting any two vertices of a graph with a rainbow vertex path and also verifies that the given colors produce a different rainbow code for each vertex. Locating rainbow connection number of graphs is a new mathematical concept, especially in graph theory, which combines the concepts of the rainbow vertex coloring and the partition dimension. In this paper, we determine the locating rainbow connection number of amalgamation of complete graphs.
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RIEZSA DESSYLUVIANI, SUCI. "PENENTUAN RAINBOW CONNECTION NUMBER DAN STRONG RAINBOW CONNECTION NUMBER PADA GRAF BERLIAN." Jurnal Matematika UNAND 6, no. 3 (November 3, 2017): 93. http://dx.doi.org/10.25077/jmu.6.3.93-99.2017.

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Misalkan G = (V, E) adalah suatu graf. Suatu pewarnaan c : E(G) → {1, 2, · · · , k}, k ∈ N pada graf G adalah suatu pewarnaan sisi di G sedemikian sehingga setiap sisi bertetangga boleh berwarna sama. Misalkan u, v ∈ V (G) dan P adalah suatu lintasan dari u ke v. Suatu intasan P dikatakan rainbow path jika tidak terdapat dua sisi di P berwarna sama. Graf G disebut rainbow connected dengan pewarnaan c jika untuk setiap u, v ∈ V (G) terdapat rainbow path dari u ke v. Jika terdapat k warna di G maka c adalah rainbow k-coloring. Rainbow connection number dari graf terhubung dinotasikan dengan rc(G), didefinisikan sebagai banyaknya warna minimal yang diperlukan untuk membuat graf G bersifat rainbow connected. Selanjutnya, pewarnaan c dikatakan pewarnaan-k strong rainbow, jika untuk setiap titik u dan v di V terdapat lintasan pelangi dengan panjangnya sama dengan jarak u dan v. Dalam makalah ini akan ditentukan rainbow connection number dan Strong Rainbow Connection Number pada graf Berlian dengan 2n titik. Graf Berlian, dinotasikan dengan Brn, adalah graf yang diperoleh dari graf tangga segitiga dengan 2n − 1 titik, dengan menambahkan satu titik dan beberapa sisi tertentu. Dalam makalah ini akan ditentukan rc(Brn) dan src(Brn) untuk n ≥ 4. Kata Kunci: Rainbow connection number, Strong rainbow connection number, Graf Berlian, Lintasan, Pewarnaan Rainbow
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Cheng, Patrick S. "The Rainbow Connection." Theology & Sexuality 17, no. 3 (September 2011): 235–64. http://dx.doi.org/10.1179/tas.17.3.815t2u2062265402.

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Medika, Gema Hista. "RAINBOW CONNECTION PADA BEBERAPA GRAF." Jurnal Matematika UNAND 2, no. 2 (June 10, 2013): 17. http://dx.doi.org/10.25077/jmu.2.2.17-25.2013.

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Misalkan G adalah graf terhubung tak-trivial. Denisikan pewarnaan c :E(G) ! f1; 2; :::; kg, k 2 N, dimana dua sisi yang bertetangga boleh memiliki warnayang sama. Suatu u 􀀀 v path P di G dikatakan rainbow path jika tidak ada dua sisi diP yang memiliki warna sama. Graf G dikatakan rainbow connected jika setiap dua titikyang berbeda di G dihubungkan oleh rainbow path. Pewarnaan sisi yang menyebabkan Gbersifat rainbow connected dikatakan rainbow coloring. Rainbow connection number darigraf terhubung G, ditulis rc(G), didenisikan sebagai banyaknya warna minimal yangdiperlukan untuk membuat graf G bersifat rainbow connected. Misalkan c adalah rainbowcoloring dari graf terhubung G. Untuk dua titik u dan v di G, rainbow u-v geodesic padaG adalah rainbow u-v path yang panjangnya d(u; v), dimana d(u; v) adalah jarak antarau dan v (panjang u-v path terpendek di G). Graf G dikatakan strongly rainbow-connectedjika G memiliki suatu rainbow u-v geodesic untuk setiap dua titik u dan v di G. Mini-mum k yang terdapat pada pewarnaan c : E(G) ! f1; 2; :::; kg sedemikian sehingga Gadalah strongly rainbow-connected dikatakan strong rainbow connection number, src(G);di G. Jadi, rc(G) src(G) untuk setiap graf terhubung di G. Pada paper ini akan di-ulas kembali tentang strong rainbow connection number dari graf bipartit lengkap Ks;tdengan 1 s t dimana s; t 2 N adalah src(Ks;t) = d spte, sedangkan rainbow connec-tion number dari graf bipartit lengkap Ks;t dengan 2 s t dimana s; t 2 N adalahrc(Ks;t) = minfd spte; 4g.
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Maretha, Ayu Nanie, Muhammad Mahfuzh Shiddiq, and Na'imah Hijriati. "BILANGAN RAINBOW CONNECTION PADA GRAF-H." EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN 15, no. 1 (July 16, 2021): 13. http://dx.doi.org/10.20527/epsilon.v15i1.3174.

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Pada teori graf terdapat konsep pewarnaan yaitu pewarnaan sisi dan pewarnaan titik. Apabila ada dua titik yang terhubung oleh lintasan rainbow maka pewarnaan sisi graf disebut rainbow connected. Bilangan rainbow connection yang dinotasikan dengan rc(G) adalah bilangan terkecil dari warna yang dibutuhkan agar terbentuk graf bersifat rainbow connected. Pewarnaan titik pada graf disebut rainbow connected jika sebarang dua titik pada graf berwarna titik dihubungkan oleh lintasan rainbow vertex. Bilangan rainbow vertex connection yang dinotasikan dengan rvc(G) adalah bilangan terkecil dari warna yang dibutuhkan agar terbentuk graf bersifat rainbow vertex connected. Graf- merupakan graf yang berbentuk seperti huruf . Operasi korona merupakan cara untuk menghasilkan dua buah graf menjadi suatu graf baru. Tujuan dari penelitian ini adalah menentukan bilangan rainbow connection dan bilangan rainbow vertex connection pada graf-H. Hasil penelitian yang diperoleh yaitu bilangan rainbow connection pada graf-H yaitu 2n-1 , bilangan rainbow vertex connection pada graf-H yaitu 2n-4 dan bilangan rainbow vertex connection pada graf H korona mK_1 adalah 2n.
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Asmara, Dwi Novri, Syafrizal Sy ., and Effendi . "BILANGAN RAINBOW CONNECTION DAN STRONG RAINBOW CONNECTION PADA GRAF JAHANGIR J 2;m." Jurnal Matematika UNAND 7, no. 1 (February 14, 2018): 64. http://dx.doi.org/10.25077/jmu.7.1.64-69.2018.

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untuk n 2, m 2 adalah suatu graf dengan(nm + 1) titik yaitu graf yang terdiri dari satu Cycle (CAbstrak. Suatu Graf Jahangir J(n;m)) dengan menambahkan satutitik yang bertetangga ke m titik dari Cnmnmyang berjarak n satu sama lain di C. Suatugraf dikatakan rainbow connected, jika setiap lintasan yang menghubungkan dua titik u; vdi G memuat rainbow u-v path dan suatu graf dikatakan strong rainbow connected, yangjika terdapat suatu lintasan dengan panjang d(u; v) yang menghubungkan dua titik u; vmemuat rainbow u-v geodesic. Pada makalah ini diperoleh rc(J2;m) dan src(J) untuk2 m 8.Kata Kunci: Graf Jahangir, rainbow connection number, strong rainbow connection numbernm2;m
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Wijaya, Reni. "BILANGAN RAINBOW CONNECTION UNTUK GRAF KOMPLEMEN." Jurnal Matematika UNAND 2, no. 3 (September 10, 2013): 9. http://dx.doi.org/10.25077/jmu.2.3.9-12.2013.

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Misalkan terdapat dua titik u, v pada graf G. Suatu u-v path, dinotasikandengan uPv di G, dikatakan rainbow path jika tidak terdapat dua sisi di P yang memiliki warna sama. Suatu pewarnaan sisi di G dikatakan rainbow connected jika setiapdua titik yang berbeda dihubungkan oleh rainbow path. Bilangan rainbow connectiondari graf terhubung G, ditulis rc(G), didefinisikan sebagai banyaknya warna minimalyang diperlukan untuk membuat G bersifat rainbow connected. Pada tulisan ini dibahastentang bilangan rainbow connection untuk komplemen dari graf lingkaran Cn dengann ≥ 6 dan graf buku B 2.
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Muchlian, Melvi. "BILANGAN RAINBOW CONNECTION UNTUK BEBERAPA GRAF THORN." Jurnal Matematika UNAND 5, no. 3 (August 30, 2016): 65. http://dx.doi.org/10.25077/jmu.5.3.65-76.2016.

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Abstrak. Misalkan G = (V (G);E(G)) adalah suatu graf terhubung tak trivial. Denisipewarnaan c : E(G) ! f1; 2; ; kg; k 2 N, dimana dua sisi yang bertetangga bolehberwarna sama. Suatu lintasan u 􀀀 v path P di G dinamakan rainbow path jika tidakterdapat dua sisi di P yang berwarna sama. Graf G disebut rainbow connected jikasetiap dua titik yang berbeda di G dihubungkan oleh rainbow path. Pewarnaaan sisiyang menyebabkan G bersifat rainbow connected dikatakan rainbow coloring. Bilan-gan Rainbow connection dari graf terhubung G, ditulis rc(G), didenisikan sebagaibanyaknya warna minimal yang diperlukan untuk membuat graf G bersifat rainbow con-nected. Misalkan c adalah rainbow coloring dari graf terhubung G. Untuk dua titik udan v di G, rainbow u􀀀v geodesic pada G adalah rainbow u􀀀v path yang panjangnyad(u; v) dimana d(u; v) adalah jarak antara u dan v (panjang u 􀀀 v path terpendek di(G). Graf G dikatakan strongly rainbow connected jika G memiliki suatu rainbow u 􀀀 vgeodesic untuk setiap dua titik u dan v di G.Minimum k yang terdapat pada pewar-naan c : E(G) ! f1; 2; ; kg sedemikian sehingga G adalah strongly rainbow connecteddikatakan bilangan strong rainbow connection, src(G), di G. Jadi, rc(G) src(G) un-tuk setiap graf terhubung di G. Pada paper ini akan diulas kembali tentang BilanganRainbow Connection untuk Beberapa Graf Thorn.
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Derindo, Haves, Lyra Yulianti, and Syafrizal Sy . "BILANGAN STRONG RAINBOW CONNECTION PADA GRAF BEADED WHEEL." Jurnal Matematika UNAND 7, no. 1 (February 14, 2018): 76. http://dx.doi.org/10.25077/jmu.7.1.76-84.2018.

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Abstrak. Suatu graf dikatakan bersifat strong rainbow connected, jika untuk setiap duatitik u dan v, lintasan rainbow antara kedua titik tersebut adalah lintasan geodesic,yaitu lintasan dengan panjang d(u; v). Graf Beaded Wheel, dinotasikan dengan BW,untuk m 3, didenisikan sebagai suatu graf dengan 2m + 1 titik, yang diperolehdengan cara menambahkan satu titik pada setiap jari-jari yang ada pada graf roda W,untuk m 3. Graf BW, untuk m 3, didenisikan dengan cara serupa, yaitu denganmenambahkan dua titik pada setiap jari-jari yang ada pada graf roda W3;m, untuk m 3.Cara menentukan bilangan strong rainbow connection untuk BW2;mmdan BWadalahdengan mendenisikan pewarnaan terhadap semua sisi pada graf sedemikian sehinggagraf tersebut bersifat strong rainbow connected. Untuk m = 4, pada tulisan ini diperolehbilangan strong rainbow connection pada graf Beaded Wheel yaitu, src(BW) = 4 dansrc(BW3;4) = 5.Kata Kunci: Beaded Wheel, strong rainbow connection3;m2;42;mm
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Dissertations / Theses on the topic "Rainbow Connection"

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Liang, Yu-Jung, and 梁育榮. "Rainbow connection numbers of Cartesian product of graphs." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/4xzvg3.

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碩士
國立東華大學
應用數學系
100
Given a connected graph G together with a coloring f from the edge set of G to a set of colors, where adjacent edges may be colored the same, a u-v path P in G is said to be a rainbow path if no two edges of P are colored the same. A u-v path P in G is said to be a rainbow u-v geodesic in G if P is a rainbow u-v path whose length equals to the distance of u and v. The graph G is rainbow-connected(resp., strongly rainbow-connected) if G contains a rainbow u-v path(resp,. rainbow u-v geodesic) for every two vertices u and v of G. In this case, the coloring f is called a rainbow coloring(resp,. strong rainbow coloring) of G. A rainbow coloring(resp., strong rainbow coloring) of G using k colors is a rainbow k-coloring(resp., strong rainbow k-coloring) of G. The minimum k for which there exists a rainbow k-coloring(resp., strong rainbow k-coloring) of G is called the rainbow connection number(resp., strong rainbow connection number) of G and is denoted by rc(G)(resp., src(G)). We study the rainbow connection numbers and the strong rainbow connection numbers of Cartesian product of graphs, where both of the two graphs are in F={G:G is a path, a cycle, or a complete graph}, or both of the two graphs are in T={T:T is a tree}, in this thesis. We show that if G is the Cartesian product of two graphs G₁ and G₂, in F, then diam(G)=rc(G)=src(G), except that both G₁ and G₂ are odd cycles. And we prove that if G is the Cartesian product of two trees T₁ and T₂, then rc(G)=diam(G), except that T₂ is the path P₂, and T₁ satisfies some special conditions, in which case the rainbow connection number of G equals diam(G)+1.
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Arunselvan, R. "Rainbow Connection Number Of Graph Power And Graph Products." Thesis, 2011. https://etd.iisc.ac.in/handle/2005/2383.

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The minimum number of colors required to color the edges of a graph so that any two distinct vertices are connected by at least one path in which no two edges are colored the same is called its rainbow connection number. This graph parameter was introduced by Chartrand et al. in 2008. The problem has garnered considerable interest and several variants of the initial version have since been introduced. The rainbow connection number of a connected graph G is denoted by rc(G). It can be shown that the rainbow connection number of a tree on n vertices is n -1. Hence |G|-1 is an upper bound for rc(G)of any non-trivial graph G. For all non-trivial, bridge-less and connected graphs G, Basavaraju etal. Showed that rc(G) can be upper-bounded by a quadratic function of its radius. In addition they also proved the tightness of the bound. It is clear that we cannot hope to get an upper-bound better than |G| - 1 in the case of graphs with bridges. An immediate and natural question is the following: Are there classes of bridge-less graphs whose rainbow connection numbers are linear functions of their radii? This question is of particular interest since the diameter is a trivial lower bound for rc(G). We answer in affirmative to the above question. In particular we studied three (graph) product operations (Cartesian, Lexicographic and Strong) and the graph powering operation. We were able to show that the rainbow connection number of the graph resulting from any of the above graph operations is upper-bounded by 2r(G)+c, where r(G) is radius of the resultant graph and c ε {0, 1, 2}.
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Arunselvan, R. "Rainbow Connection Number Of Graph Power And Graph Products." Thesis, 2011. http://etd.iisc.ernet.in/handle/2005/2383.

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The minimum number of colors required to color the edges of a graph so that any two distinct vertices are connected by at least one path in which no two edges are colored the same is called its rainbow connection number. This graph parameter was introduced by Chartrand et al. in 2008. The problem has garnered considerable interest and several variants of the initial version have since been introduced. The rainbow connection number of a connected graph G is denoted by rc(G). It can be shown that the rainbow connection number of a tree on n vertices is n -1. Hence |G|-1 is an upper bound for rc(G)of any non-trivial graph G. For all non-trivial, bridge-less and connected graphs G, Basavaraju etal. Showed that rc(G) can be upper-bounded by a quadratic function of its radius. In addition they also proved the tightness of the bound. It is clear that we cannot hope to get an upper-bound better than |G| - 1 in the case of graphs with bridges. An immediate and natural question is the following: Are there classes of bridge-less graphs whose rainbow connection numbers are linear functions of their radii? This question is of particular interest since the diameter is a trivial lower bound for rc(G). We answer in affirmative to the above question. In particular we studied three (graph) product operations (Cartesian, Lexicographic and Strong) and the graph powering operation. We were able to show that the rainbow connection number of the graph resulting from any of the above graph operations is upper-bounded by 2r(G)+c, where r(G) is radius of the resultant graph and c ε {0, 1, 2}.
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Guo–Shi, Sung, and 宋國璽. "A Study on the Rainbow Connection of Triangular Pyramid Networks." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/94673132943668843317.

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碩士
中國文化大學
資訊管理學系
101
Rainbow connection number of a connected graph G is the minimum number of colors needed to color the edges of G, so that every pair of vertices is connected by at least one path whose edges have distinct colors. The concept of rainbow connection was introduced by Chartrand et al. in 2008. Many scholars are interested in rainbow connection problem and have results on graphs, such as wheel graphs, Peterson graphs, complete graphs, pyramid networks etc. According to the known literature, there has not yet been anyone to propose about rainbow connection number of the triangular pyramid networks. In this paper, we propose a minimum rainbow coloring for a triangular mesh. Based on the modification of the edge coloring for triangular meshes, we further determine the rainbow connection number of a triangular pyramid.
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Wu, Zejian, and 吳則建. "On Finding a Rainbow Connection in a Versatile Pyramid Network." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/90080836433079435170.

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碩士
中國文化大學
資訊管理學系
101
Edge coloring of a graph is a function from its edge set to the set of natural numbers. A path in an edge colored graph with no two edges sharing the same color is called a rainbow path. An edge-colored graph is rainbow connected if any two vertices are connected by a rainbow path. Rainbow connection number is the minimum number of colors needed to color the edges of graph. The concept of rainbow connection was introduced by Chartrand et al. in 2008. The rainbow connection problem is to find a vertex coloring for a given graph so that each pair of vertices of the graph having at least a rainbow path. As the characteristics and type of different network topologies are not the same, so we first devote ourselves to study a specify network topology. Then we find results of rainbow connection for the given graph. Some results of rainbow connection for graphs were shown by the published papers, while the results for new network topologies were lack of discussion. As far as we know, the rainbow connection on Recursive Transpose-Connected Cycles pyramid networks is unknown We consider the problem for Recursive Transpose-Connected Cycles pyramid networks, finally we propose a rainbow coloring for the RTCC pyramid networks based on 4-cycles. Then an upper bound of rainbow connection number is established for our studied interconnection networks.
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Rajendraprasad, Deepak. "Rainbow Colouring and Some Dimensional Problems in Graph Theory." Thesis, 2013. https://etd.iisc.ac.in/handle/2005/3336.

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This thesis touches three different topics in graph theory, namely, rainbow colouring, product dimension and boxicity. Rainbow colouring An edge colouring of a graph is called a rainbow colouring, if every pair of vertices is connected by atleast one path in which no two edges are coloured the same. The rainbow connection number of a graph is the minimum number of colours required to rainbow colour it. In this thesis we give upper bounds on rainbow connection number based on graph invariants like minimum degree, vertex connectivity, and radius. We also give some computational complexity results for special graph classes. Product dimension The product dimension or Prague dimension of a graph G is the smallest natural number k such that G is an induced subgraph of a direct product of k complete graphs. In this thesis, we give upper bounds on the product dimension for forests, bounded tree width graphs and graphs of bounded degeneracy. Boxicity and cubicity The boxicity (cubicity of a graph G is the smallest natural number k such that G can be represented as an intersection graph of axis-parallel rectangular boxes(axis-parallel unit cubes) in Rk .In this thesis, we study the boxicity and the cubicity of Cartesian, strong and direct products of graphs and give estimates on the boxicity and the cubicity of a product graph based on invariants of the component graphs. Separation dimension The separation dimension of a hypergraph H is the smallest natural number k for which the vertices of H can be embedded in Rk such that any two disjoint edges of H can be separated by a hyper plane normal to one of the axes. While studying the boxicity of line graphs, we noticed that a box representation of the line graph of a hypergraph has a nice geometric interpretation. Hence we introduced this new parameter and did an extensive study of the same.
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Rajendraprasad, Deepak. "Rainbow Colouring and Some Dimensional Problems in Graph Theory." Thesis, 2013. http://etd.iisc.ernet.in/2005/3336.

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This thesis touches three different topics in graph theory, namely, rainbow colouring, product dimension and boxicity. Rainbow colouring An edge colouring of a graph is called a rainbow colouring, if every pair of vertices is connected by atleast one path in which no two edges are coloured the same. The rainbow connection number of a graph is the minimum number of colours required to rainbow colour it. In this thesis we give upper bounds on rainbow connection number based on graph invariants like minimum degree, vertex connectivity, and radius. We also give some computational complexity results for special graph classes. Product dimension The product dimension or Prague dimension of a graph G is the smallest natural number k such that G is an induced subgraph of a direct product of k complete graphs. In this thesis, we give upper bounds on the product dimension for forests, bounded tree width graphs and graphs of bounded degeneracy. Boxicity and cubicity The boxicity (cubicity of a graph G is the smallest natural number k such that G can be represented as an intersection graph of axis-parallel rectangular boxes(axis-parallel unit cubes) in Rk .In this thesis, we study the boxicity and the cubicity of Cartesian, strong and direct products of graphs and give estimates on the boxicity and the cubicity of a product graph based on invariants of the component graphs. Separation dimension The separation dimension of a hypergraph H is the smallest natural number k for which the vertices of H can be embedded in Rk such that any two disjoint edges of H can be separated by a hyper plane normal to one of the axes. While studying the boxicity of line graphs, we noticed that a box representation of the line graph of a hypergraph has a nice geometric interpretation. Hence we introduced this new parameter and did an extensive study of the same.
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Books on the topic "Rainbow Connection"

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Fletcher, Peggy. Rainbow connection. Sarnia, Ont: River City Press, 1996.

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Carlino, Cristina. The rainbow connection. New York: Doubleday, 1999.

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Marambio, Rodrigo Salinas. The rainbow connection: Rodrigo Salinas. Santiago, Chile: D21 Galería de Arte, 2012.

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Stein, Jessica Max. The rainbow connection: Richard Hunt, gay Muppeteer. Brooklyn, NY: Long Walk Press, 2009.

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Johns, Michael-Anne. Mariah Carey: Your rainbow connection to today's most popular singer! New York: Scholastic, 2000.

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Li, Xueliang, and Yuefang Sun. Rainbow Connections of Graphs. Boston, MA: Springer US, 2012. http://dx.doi.org/10.1007/978-1-4614-3119-0.

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waters, vera. Rainbow connections: True reflections. Oldham: Penn Cottage Books, 2012.

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Li, Xueliang. Rainbow Connections of Graphs. Boston, MA: Springer US, 2012.

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Council, Northern Alberta Development. Connecting Northwest Canada--: Linking Fort Nelson, British Columbia and Rainbow lake, Alberta. Edmonton, Alta.]: The Council, 2001.

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Ascher, Kenny, and Paul Williams. Rainbow Connection. Hal Leonard Publishing Corporation, 1986.

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Book chapters on the topic "Rainbow Connection"

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Li, Xueliang, and Yuefang Sun. "Rainbow Vertex-Connection Number." In SpringerBriefs in Mathematics, 89–96. Boston, MA: Springer US, 2012. http://dx.doi.org/10.1007/978-1-4614-3119-0_8.

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Li, Xueliang, and Yuefang Sun. "Upper Bounds for Rainbow Connection Numbers." In SpringerBriefs in Mathematics, 25–55. Boston, MA: Springer US, 2012. http://dx.doi.org/10.1007/978-1-4614-3119-0_3.

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Li, Xueliang, and Yuefang Sun. "Rainbow Connection Numbers of Graph Products." In SpringerBriefs in Mathematics, 73–76. Boston, MA: Springer US, 2012. http://dx.doi.org/10.1007/978-1-4614-3119-0_6.

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Bitterman, Alex. "The Rainbow Connection: A Time-Series Study of Rainbow Flag Display Across Nine Toronto Neighborhoods." In The Life and Afterlife of Gay Neighborhoods, 117–37. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-66073-4_5.

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AbstractRecently, the display and use of the rainbow flag in historically defined gay neighborhoods has grown even as gay residents and businesses have been driven away by gentrification, rising real-estate costs, and cultural homogenization. At the same time, prevelence and use of the rainbow flag and the rainbow motif has increased in areas not usually considered part of recognized gay neighborhoods. This chapter explores the prevalence and persistence of the display of the rainbow flag and rainbow motif in nine neighborhoods across Toronto, Ontario, Canada. The visual assessment of rainbow flag use across these neighborhoods serves as a potential model for examining the rate of spread of rainbow flags and visual rainbow motif symbols as a means for tracking the movement of the LGBTQ+ community across urban neighborhoods. Initial results suggest potential significance of the prevalence and persistence of the rainbow flag and the rainbow motif. These include; (1) a possible diaspora of LGBTQ+ residents from traditionally defined gay neighborhoods to newly emerging gay or LGBTQ-friendly neighborhoods, (2) a newfound inclusivity or pride among residents of other neighborhoods, and (3) “rainbow washing” due to overuse of the rainbow motif by non-LGBTQ businesses and organizations connected with pride celebrations. While overuse of the rainbow flag may diminish historically coded meaning of the rainbow, that well-intentioned use of the rainbow flag is a positive and welcoming indicator for LGBTQ+ individuals and it may lead to the emergence of additional LGBTQ-friendly enclaves that, over time, could potentially emerge as new gay neighborhoods.
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Li, Xueliang, and Yuefang Sun. "Rainbow Connection Numbers of Some Graph Classes." In SpringerBriefs in Mathematics, 65–72. Boston, MA: Springer US, 2012. http://dx.doi.org/10.1007/978-1-4614-3119-0_5.

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Sun, Yuefang. "Rainbow Connection Numbers for Undirected Double-Loop Networks." In Springer Proceedings in Mathematics & Statistics, 109–16. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-08377-3_12.

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Schiermeyer, Ingo. "Rainbow Connection in Graphs with Minimum Degree Three." In Lecture Notes in Computer Science, 432–37. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-10217-2_42.

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Wang, Fu-Hsing, Ze-Jian Wu, and Yann-Jong Hwang. "An Upper Bound of the Rainbow Connection Number in RTCC Pyramids." In Advances in Intelligent Systems and Applications - Volume 1, 15–23. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-35452-6_3.

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Parmar, Dharamvirsinh, and Bharat Suthar. "Rainbow Vertex Connection Number of a Class of Triangular Snake Graph." In Recent Advancements in Graph Theory, 329–38. Boca Raton : CRC Press, 2020. | Series: Mathematical engineering, manufacturing, and management sciences: CRC Press, 2020. http://dx.doi.org/10.1201/9781003038436-27.

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Oakenfull, Gillian. "Making the Rainbow Connection: Factors Influencing Gay Consumers’ Evaluations of Gay-Friendly Corporate Activities." In Marketing Dynamism & Sustainability: Things Change, Things Stay the Same…, 429. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-10912-1_142.

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Conference papers on the topic "Rainbow Connection"

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Lubis, H., N. M. Surbakti, R. I. Kasih, D. R. Silaban, and K. A. Sugeng. "Rainbow connection and strong rainbow connection of the crystal graph and neurons graph." In PROCEEDINGS OF THE 4TH INTERNATIONAL SYMPOSIUM ON CURRENT PROGRESS IN MATHEMATICS AND SCIENCES (ISCPMS2018). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5132480.

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Wang, Fu-Hsing, and Cheng-Ju Hsu. "Rainbow Connection Number in Pyramid Networks." In the 11th International Conference. New York, New York, USA: ACM Press, 2019. http://dx.doi.org/10.1145/3307363.3307405.

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Susilawati and A. N. M. Salman. "Rainbow connection number of rocket graphs." In THE 5TH INTERNATIONAL CONFERENCE ON MATHEMATICS AND NATURAL SCIENCES. AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4930634.

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Hasan, M. Ali, Risma Yulina Wulandari, and A. N. M. Salman. "Rainbow Connection Number of Shackle Graphs." In International Conference on Mathematics, Geometry, Statistics, and Computation (IC-MaGeStiC 2021). Paris, France: Atlantis Press, 2022. http://dx.doi.org/10.2991/acsr.k.220202.013.

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Rocha, Aleffer, Sheila M. Almeida, and Leandro M. Zatesko. "The Rainbow Connection Number of Triangular Snake Graphs." In Encontro de Teoria da Computação. Sociedade Brasileira de Computação - SBC, 2020. http://dx.doi.org/10.5753/etc.2020.11091.

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Rainbow coloring problems, of noteworthy applications in Information Security, have been receiving much attention last years in Combinatorics. The rainbow connection number of a graph G is the least number of colors for a (not necessarily proper) edge coloring of G such that between any pair of vertices there is a path whose edge colors are all distinct. In this paper we determine the rainbow connection number of the triple triangular snake graphs.
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Arputhamary, I. Annammal, and M. Helda Mercy. "Strong rainbow vertex-connection of cubic graphs." In 2015 IEEE 9th International Conference on Intelligent Systems and Control (ISCO). IEEE, 2015. http://dx.doi.org/10.1109/isco.2015.7282240.

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Shulhany, M. A., and A. N. M. Salman. "The (strong) rainbow connection number of stellar graphs." In PROCEEDINGS OF INTERNATIONAL SEMINAR ON MATHEMATICS, SCIENCE, AND COMPUTER SCIENCE EDUCATION (MSCEIS 2015). AIP Publishing LLC, 2016. http://dx.doi.org/10.1063/1.4941170.

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Bustan, Ariestha Widyastuty, and A. N. M. Salman. "The rainbow vertex connection number of star wheel graphs." In INTERNATIONAL CONFERENCE ON SCIENCE AND APPLIED SCIENCE (ICSAS) 2019. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5141660.

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Nuriyeva, Fidan, Onur Ugurlu, and Hakan Kutucu. "A mathematical model for finding the rainbow connection number." In 2013 7th International Conference on Application of Information and Communication Technologies (AICT). IEEE, 2013. http://dx.doi.org/10.1109/icaict.2013.6722630.

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Septyanto, F., and K. A. Sugeng. "(Strong) rainbow connection on the splitting of 3-path." In INTERNATIONAL SYMPOSIUM ON CURRENT PROGRESS IN MATHEMATICS AND SCIENCES 2016 (ISCPMS 2016): Proceedings of the 2nd International Symposium on Current Progress in Mathematics and Sciences 2016. Author(s), 2017. http://dx.doi.org/10.1063/1.4991235.

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