Relevant bibliographies by topics / Connection graph

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Academic literature on the topic 'Connection graph'

Author: Grafiati
Published: 25 May 2024

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Journal articles on the topic "Connection graph"

1

Ismail, Sumarno, Isran K. Hasan, Tesya Sigar, and Salmun K. Nasib. "RAINBOW CONNECTION NUMBER AND TOTAL RAINBOW CONNECTION NUMBER OF AMALGAMATION RESULTS DIAMOND GRAPH(〖Br〗_4) AND FAN GRAPH(F_3)." BAREKENG: Jurnal Ilmu Matematika dan Terapan 16, no. 1 (2022): 023–30. http://dx.doi.org/10.30598/barekengvol16iss1pp023-030.

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If be a graph and edge coloring of G is a function , rainbow connection number is the minimum-k coloration of the rainbow on the edge of graph G and denoted by rc(G). Rainbow connection numbers can be applied to the result of operations on some special graphs, such as diamond graphs and fan graphs. Graph operation is a method used to obtain a new graph by combining two graphs. This study performed amalgamation operations to obtain rainbow connection numbers and rainbow-total-connection numbers in diamond graphs ( ) and fan graphs ( ) or . Based on the research, it is obtained that the rainbow-connection number theorem on the amalgamation result of the diamond graph ( ) and fan graph ( is with . Furthermore, the theorem related to the total rainbow-connection number on the amalgamation result of the diamond graph( ) and the fan graph ( is obtained, namely with .
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2

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 (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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3

Alrowaili, Dalal Awadh, Faiz Farid, and Muhammad Javaid. "Gutman Connection Index of Graphs under Operations." Symmetry 15, no. 1 (2022): 21. http://dx.doi.org/10.3390/sym15010021.

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In the modern era, mathematical modeling consisting of graph theoretic parameters or invariants applied to solve the problems existing in various disciplines of physical sciences like computer sciences, physics, and chemistry. Topological indices (TIs) are one of the graph invariants which are frequently used to identify the different physicochemical and structural properties of molecular graphs. Wiener index is the first distance-based TI that is used to compute the boiling points of the paraffine. For a graph F, the recently developed Gutman Connection (GC) index is defined on all the unordered pairs of vertices as the sum of the multiplications of the connection numbers and the distance between them. In this note, the GC index of the operation-based symmetric networks called by first derived graph D1(F) (subdivision graph), second derived graph D2(F) (vertex-semitotal graph), third derived graph D3(F) (edge-semitotal graph) and fourth derived graph D4(F) (total graph) are computed in their general expressions consisting of various TIs of the parent graph F, where these operation-based symmetric graphs are obtained by applying the operations of subdivision, vertex semitotal, edge semitotal and the total on the graph F respectively.
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4

ZHANG, YINGYING, and XIAOYU ZHU. "Proper Vertex Connection and Graph Operations." Journal of Interconnection Networks 19, no. 02 (2019): 1950001. http://dx.doi.org/10.1142/s0219265919500014.

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A path in a vertex-colored graph is a vertex-proper path if any two internal adjacent vertices differ in color. A vertex-colored graph is proper vertex k-connected if any two vertices of the graph are connected by k disjoint vertex-proper paths of the graph. For a k-connected graph G, the proper vertex k-connection number of G, denoted by pvck(G), is defined as the smallest number of colors required to make G proper vertex k-connected. A vertex-colored graph is strong proper vertex-connected, if for any two vertices u, v of the graph, there exists a vertex-proper u-v geodesic. For a connected graph G, the strong proper vertex-connection number of G, denoted by spvc(G), is the smallest number of colors required to make G strong proper vertex-connected. In this paper, we study the proper vertex k-connection number and the strong proper vertex-connection number on the join of two graphs, the Cartesian, lexicographic, strong and direct product, and present exact values or upper bounds for these operations of graphs. Then we apply these results to some instances of Cartesian and lexicographic product networks.
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5

Farid, Faiz, Muhammad Javaid, and Ebenezer Bonyah. "Computing Connection Distance Index of Derived Graphs." Mathematical Problems in Engineering 2022 (July 18, 2022): 1–15. http://dx.doi.org/10.1155/2022/1439177.

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Distance based topological indices (TIs) play a vital role in the study of various structural and chemical aspects for the molecular graphs. The first distance-based TI is used to find the boiling point of paraffin. The connection distance (CD) index is a latest developed TI that is defined as the sum of all the products of distances between pair of vertices with the sum of their respective connection numbers . In this paper, we computed CD indices of the different derived graphs (subdivision graph S G , vertex-semitotal graph R G , edge-semitotal graph Q G and total graph T G obtained from the graph G under various operations of subdivision in the form of degree distance (DD) and CD indices of the basic graphs including some other algebraic expressions.
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6

Javaid, Muhammad, Muhammad Khubab Siddique, and Ebenezer Bonyah. "Computing Gutman Connection Index of Thorn Graphs." Journal of Mathematics 2021 (November 15, 2021): 1–13. http://dx.doi.org/10.1155/2021/2289514.

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Chemical structural formula can be represented by chemical graphs in which atoms are considered as vertices and bonds between them are considered as edges. A topological index is a real value that is numerically obtained from a chemical graph to predict its various physical and chemical properties. Thorn graphs are obtained by attaching pendant vertices to the different vertices of a graph under certain conditions. In this paper, a numerical relation between the Gutman connection (GC) index of a graph and its thorn graph is established. Moreover, the obtained result is also illustrated by computing the GC index for the particular families of the thorn graphs such as thorn paths, thorn rods, thorn stars, and thorn rings.
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7

Lihawa, Indrawati, Sumarno Ismail, Isran K. Hasan, Lailany Yahya, Salmun K. Nasib, and Nisky Imansyah Yahya. "Bilangan Terhubung Titik Pelangi pada Graf Hasil Operasi Korona Graf Prisma (P_(m,2)) dan Graf Lintasan (P_3)." Jambura Journal of Mathematics 4, no. 1 (2022): 145–51. http://dx.doi.org/10.34312/jjom.v4i1.11826.

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Rainbow vertex-connection number is the minimum k-coloring on the vertex graph G and is denoted by rvc(G). Besides, the rainbow-vertex connection number can be applied to some special graphs, such as prism graph and path graph. Graph operation is a method used to create a new graph by combining two graphs. Therefore, this research uses corona product operation to form rainbow-vertex connection number at the graph resulting from corona product operation of prism graph and path graph (Pm,2 P3) (P3 Pm,2). The results of this study obtain that the theorem of rainbow vertex-connection number at the graph resulting from corona product operation of prism graph and path graph (Pm,2 P3) (P3 Pm,2) for 3 = m = 7 are rvc (G) = 2m rvc (G) = 2.
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8

Yahya, Nisky Imansyah, Ainun Fatmawati, Nurwan Nurwan, and Salmun K. Nasib. "RAINBOW VERTEX-CONNECTION NUMBER ON COMB PRODUCT OPERATION OF CYCLE GRAPH (C_4) AND COMPLETE BIPARTITE GRAPH (K_(3,N))." BAREKENG: Jurnal Ilmu Matematika dan Terapan 17, no. 2 (2023): 0673–84. http://dx.doi.org/10.30598/barekengvol17iss2pp0673-0684.

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Rainbow vertex-connection number is the minimum colors assignment to the vertices of the graph, such that each vertex is connected by a path whose edges have distinct colors and is denoted by . The rainbow vertex connection number can be applied to graphs resulting from operations. One of the methods to create a new graph is to perform operations between two graphs. Thus, this research uses comb product operation to determine rainbow-vertex connection number resulting from comb product operation of cycle graph and complete bipartite graph & . The research finding obtains the theorem of rainbow vertex-connection number at the graph of for while the theorem of rainbow vertex-connection number at the graph of for for .
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9

Asif, Muhammad, Bartłomiej Kizielewicz, Atiq ur Rehman, Muhammad Hussain та Wojciech Sałabun. "Study of θϕ Networks via Zagreb Connection Indices". Symmetry 13, № 11 (2021): 1991. http://dx.doi.org/10.3390/sym13111991.

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Graph theory can be used to optimize interconnection network systems. The compatibility of such networks mainly depends on their topology. Topological indices may characterize the topology of such networks. In this work, we studied a symmetric network θϕ formed by ϕ time repetition of the process of joining θ copies of a selected graph Ω in such a way that corresponding vertices of Ω in all the copies are joined with each other by a new edge. The symmetry of θϕ is ensured by the involvement of complete graph Kθ in the construction process. The free hand to choose an initial graph Ω and formation of chemical graphs using θϕΩ enhance its importance as a family of graphs which covers all the pre-defined graphs, along with space for new graphs, possibly formed in this way. We used Zagreb connection indices for the characterization of θϕΩ. These indices have gained worth in the field of chemical graph theory in very small duration due to their predictive power for enthalpy, entropy, and acentric factor. These computations are mathematically novel and assist in topological characterization of θϕΩ to enable its emerging use.
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10

Ma, Yingbin, and Kairui Nie. "Rainbow Vertex Connection Numbers and Total Rainbow Connection Numbers of Middle and Total Graphs." Ars Combinatoria 157 (December 31, 2023): 45–52. http://dx.doi.org/10.61091/ars157-04.

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A vertex-colouring of a graph Γ is rainbow vertex connected if every pair of vertices ( u , v ) in Γ there is a u − v path whose internal vertices have different colours. The rainbow vertex connection number of a graph Γ , is the minimum number of colours needed to make Γ rainbow vertex connected, denoted by r v c ( Γ ) . Here, we study the rainbow vertex connection numbers of middle and total graphs. A total-colouring of a graph Γ is total rainbow connected if every pair of vertices ( u , v ) in Γ there is a u − v path whose edges and internal vertices have different colours. The total rainbow connection number of Γ , is the minimum number of colours required to colour the edges and vertices of Γ in order to make Γ total rainbow connected, denoted by t r c ( Γ ) . In this paper, we also research the total rainbow connection numbers of middle and total graphs.
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