Bilangan Terhubung Titik Pelangi pada Graf Hasil Operasi Korona Graf Prisma (P_(m,2)) dan Graf Lintasan (P_3)

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.

On Rainbow Vertex Antimagic Coloring of Graphs: A New Notion

All graph in this paper are simple, finite, and connected. Let be a labeling of a graph . The function is called antimagic rainbow edge labeling if for any two vertices and , all internal vertices in path have different weight, where the weight of vertex is the sum of its incident edges label. The vertex weight denoted by for every . If G has a antimagic rainbow edge labeling, then is a antimagic rainbow vertex connection, where the every vertex is assigned with the color . The antimagic rainbow vertex connection number of , denoted by , is the minimum colors taken over all rainbow vertex connection induced by antimagic rainbow edge labeling of . In this paper, we determined the exact value of the antimagic rainbow vertex connection number of path ( ), wheel ( ), friendship ( ), and fan ( ).

Dynamic evaluation of regional water resources carrying capacity based on set pair analysis and partial connection number

In order to describe the micro motion between the connection number components and seek a more applicable evaluation model, quantitatively evaluate and analyze regional water resources carrying capacity (WRCC). Firstly, an evaluation index system and grade standards of regional WRCC were constructed. Then, a method for determining the connection number was proposed, which considered the micro motion between the connection number components in system structure. Finally, built an evaluation model based on set pair analysis (SPA) and partial connection number (PCN) that used subtraction set pair potential (SPP) to identify vulnerability factors, and identification results were compared with total partial connection number (TPCN). The model was applied to Huaibei City, Anhui Province, China. The results showed that: the WRCC grade value was between 2 and 3 that was poor; the support and regulation subsystem grade value was between 2 and 3, and the pressure subsystem grade value was between 1 and 2. SPP identified that the support force and regulation force subsystem were the vulnerable subsystems. Eight indexes such as water resources per capita, rate of ecological water consumption and density of population were the main indicators causing the poor WRCC, which were in good agreement with the local measured data. In addition, the SPP and TPCN are compared to further verify rationality of the connection number determination method and reliability of the identification results. The model established in this paper has strong applicability and can also be used for the dynamic evaluation of other resources, environment and ecological carrying capacity. The results in this study can provide a scientific basis for water resources management and decision-making.

A NOTE ON GENERALIZED RAINBOW CONNECTION OF CONNECTED GRAPHS AND THEIR NUMBER OF EDGES

Let l ≥ 1, k ≥ 1 be two integers. Given an edge-coloured connected graph G. A path P in the graph G is called l-rainbow path if each subpath of length at most l + 1 is rainbow. The graph G is called (k, l)-rainbow connected if any two vertices in G are connected by at least k pairwise internally vertex-disjoint l-rainbow paths. The smallest number of colours needed in order to make G (k, l)-rainbow connected is called the (k, l)-rainbow connection number of G and denoted by rck,l(G). In this paper, we first focus to improve the upper bound of the (1, l)-rainbow connection number depending on the size of connected graphs. Using this result, we characterize all connected graphs having the large (1, 2)-rainbow connection number. Moreover, we also determine the (1, l)-rainbow connection number in a connected graph G containing a sequence of cut-edges.

Recognition Method of Vehicle Cluster Situation Based on Set Pair Logic considering Driver’s Cognition

The recognition of vehicle cluster situations is one of the critical technologies of advanced driving, such as intelligent driving and automated driving. The accurate recognition of vehicle cluster situations is helpful for behavior decision-making safe and efficient. In order to accurately and objectively identify the vehicle cluster situation, a vehicle cluster situation model is proposed based on the interval number of set pair logic. The proposed model can express the traffic environment’s knowledge considering each vehicle’s characteristics, grouping relationships, and traffic flow characteristics in the target vehicle’s interest region. A recognition method of vehicle cluster situation is designed to infer the traffic environment and driving conditions based on the connection number of set pair logic. In the proposed model, the uncertainty of the driver’s cognition is fully considered. In the recognition method, the relative uncertainty and relative certainty of driver’s cognition, traffic information, and vehicle cluster situation are fully considered. The verification results show that the proposed recognition method of vehicle cluster situations can realize accurate and objective recognition. The proposed anthropomorphic recognition method could provide a basis for vehicle autonomous behavior decision-making.

Study of Generalized Hourglass Section in Carbon Nanocone via Connection Number

In 1972, Gutman and Trinajstic showed that total π -energy of a molecule depends upon a numeric quantity which is often called as Zagreb index. In the same report, they also discussed another numeric quantity depending on the number of atoms at a distance two from a particular atom and proved influencing results on π -energy of a molecule. In modern literature, this quantity is named as connection number. In this article, we will describe some Zagreb connection numbers for hourglass section in carbon nanocone network with different lengths of cycle in the central core.

Total Proper Connection and Graph Operations

A graph is said to be total-colored if all the edges and vertices of the graph are colored. A path in a total-colored graph is a total proper path if (i) any two adjacent edges on the path differ in color, (ii) any two internal adjacent vertices on the path differ in color, and (iii) any internal vertex of the path differs in color from its incident edges on the path. A total-colored graph is called total-proper connected if any two vertices of the graph are connected by a total proper path of the graph. For a connected graph [Formula: see text], the total proper connection number of [Formula: see text], denoted by [Formula: see text], is defined as the smallest number of colors required to make [Formula: see text] total-proper connected. In this paper, we study the total proper connection number for the graph operations. We find that 3 is the total proper connection number for the join, the lexicographic product and the strong product of nearly all graphs. Besides, we study three kinds of graphs with one factor to be traceable for the Cartesian product as well as the permutation graphs of the star and traceable graphs. The values of the total proper connection number for these graphs are all [Formula: see text].