Journal of Combinatorial Mathematics and Combinatorial Computing

ISSN: 0835-3026 (print) 2817-576X (online)

The Journal of Combinatorial Mathematics and Combinatorial Computing (JCMCC) embarked on its publishing journey in April 1987. From 2024 onward, it publishes four volumes per year in March, June, September and December. JCMCC has gained recognition and visibility in the academic community and is indexed in renowned databases such as MathSciNet, Zentralblatt, Engineering Village and Scopus. The scope of the journal includes; Combinatorial Mathematics, Combinatorial Computing, Artificial Intelligence and applications of Artificial Intelligence in various files.

Fanghua Guo1,2, Yanbo Zhang1,2, Yunqing Zhang3
1School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China
2Hebei Research Center of the Basic Discipline Pure Mathematics, Shijiazhuang 050024, China
3School of Mathematics, Nanjing University, Nanjing 210093, China
Abstract:

Given two graphs G1 and G2, the size Ramsey number r^(G1,G2) refers to the smallest number of edges in a graph G such that for any red-blue edge-coloring of G, either a red subgraph G1 or a blue subgraph G2 is present in G. If we further restrict the host graph G to be connected, we obtain the connected size Ramsey number, denoted as r^c(G1,G2). Erd\H{o}s and Faudree (1984) proved that r^(nK2,K1,m)=mn for all positive integers m,n. In this paper, we concentrate on the connected analog of this result. Rahadjeng, Baskoro, and Assiyatun (2016) provided the exact values of r^c(nK2,K1,m) for n=2,3. We establish a more general result: for all positive integers m and n with mn2+2pn+n32, we have r^c(nK1,p,K1,m)=n(m+p)1. As a corollary, r^c(nK2,K1,m)=nm+n1 for mn2+3n32. We also propose a conjecture for the interested reader.

H. D. Vadhel1, M. R. Jadeja2
1Department of Mathematics, Dr. Shubhash University, Junagadh-362 001, Gujarat, India
2Department of AI, ML and DS, Marwadi University, Rajkot – 360 003, Gujarat, India
Abstract:

A subset SV(G) is called a captive dominating set of a graph G if S is a total dominating set and every vertex vS is adjacent to at least one vertex which is not in S. Furthermore, a captive dominating set S is termed a minimal captive dominating set if no proper subset SS qualifies as a captive dominating set. The minimum size of such captive dominating set in G is referred to as the captive domination number of G, denoted by γca(G). This paper investigates the relationship between the captive domination number and the order of a graph. We establish bounds on the captive domination number and present results for specific graph families obtained through various graph operations.

LeRoy B. Beasley1
1Dept. of Mathematics and Statistics, Utah State University, Logan, Utah
Abstract:

LetG be an undirected graph. A tree partition ofG is a set of trees whose edge sets are disjoint and whose union is the edge set ofG. The minimum cardinality of such a tree partition is called the tree partition number ofG. We show that for various types of trees allowed in the tree partition, that the only linear operators that preserve the tree partition number are vertex permutations.

Fatima Asif1, Agha Kashif1, Sohail Zafar1, Michael Onyango Ojiema2
1Department of Mathematics, University of Management and Technology (UMT), Lahore, Pakistan
2Masinde Muliro University of Science and Technology, Kenya
Abstract:

The Mostar index MoI of a finite and connected graph G is a measure of asymmetry, focusing on the edge-based structure of the graph. For an edge xy in G, let γxy and γyx denote the cardinalities of the sets of vertices closer to x and y respectively, then the Mostar index is defined as: MoI(G)=xyE(G)|γxyγyx| where the summation is taken over all edges xyG. This edge-wise difference reflects how asymmetrically the graph is structured around each edge and summing these differences across all edges yields the Mostar index for the graph. In this article, we compute the MoI for certain classes of bicyclic graphs that are of particular interest due to their moderately complex structure, lying between acyclic and polycyclic graphs. We classify bicyclic graphs into three distinct types, namely B1(m,n),B2(l,m,n) and B1(l,m), based on their cycle arrangements and then provide explicit formulas for calculating the exact value of the Mostar index.

S. Beatrice1, Janaki Meena M1, Dhivviyanandam I2
1School of Computer Science and Engineering Department, Vellore Institute of Technology, Chennai-600127
2Department of Mathematics, North Bengal St. Xavier’s College, Rajganj, West Bengal, India
Abstract:

Alzheimer’s disease (AD) is a progressive neurodegenerative condition that affects the elderly population. The early detection and diagnosis of AD is critical for achieving effective treatment, as it can greatly improve the patient experience. AD can be viewed through imaging techniques like MRI, PET, and SPECT, providing valuable information about structural and functional changes. These findings are important in understanding this area. However, each imaging modality offers a different perspective. This information can be better collected from several of the other modalities as well as from some others to improve accuracy and reliability in AD detection. By combining information from different imaging modalities, such as MRI, PET, DTI, and fMRI, automated multimodal medical image frameworks aim to create a fused representation that preserves the relevant features from each modality. Convolutional neural networks (CNNs) and generative adversarial networks (GANs), among other deep learning techniques, have been prevalent in these frameworks for learning discriminative and informative features from multi-modal data. In this paper, The Alzheimer’s Disease Neuroimaging Initiative (ADNI) is used for experimental analysis. The proposed work gives 98.94% of accuracy and 1.06% of error which is greater than the existing approaches.

Zhour Oumazouz1
1Laboratory of mathematics, computer science and applications, Faculty of Science and Technology, Hassan II university, Mohammedia, Morocco
Abstract:

The power of the public key cryptosystem based on Paley graphs is due to several mathematical problems namely quadratic residuosity, local equivalence, and identification of the graphs induced by a sequence of local complementations of the Paley graphs. The classification in terms of degree of these induced graphs can be useful in the cryptanalysis part of the proposed public-key cryptosystem based on these algebraic graphs. This work aims to give the exact value of the minimum and maximum degree by local complementation, then the possible classifications in terms of degree to the graphs induced by a sequence of local complementations of Paley graphs of degree p less than or equal to 13 and some information about the equivalence problem.

Bijo S. Anand1, Arun Anil2, Manoj Changat2, Prasanth G. Narasimha-Shenoi3,4, Sabeer S. Ramla5
1Department of Mathematics, Sree Narayana College, Punalur, Kollam, Kerala, India – 691305
2Department of Futures Studies, University of Kerala,Thiruvananthapuram, Kerala, India – 695581
3Department of Mathematics, Government College Chittur, Palakkad, Kerala, India – 678104
4Department of Collegiate Education, Government of Kerala, Thiruvananthapuram, Kerala, India – 695033
5Department of Mathematics, Thangal Kunju Musaliar Institute of Technology, Musaliar Hills, Karuvelil P.O., Ezhukone, Kollam, Kerala, India – 691505
Abstract:

Given a graph G, a set is Δ convex if there is no vertex uV(G)S that forms a triangle with two vertices of S. The Δ-convex hull of S is the minimum Δ-convex set containing S. This article is an attempt to discuss the Carath\’eodory number and exchange number on various graph families and standard graph products namely Cartesian, strong and lexicographic products of graphs.

Yang Zhang1, Liwei Zeng2
1Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China
2College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, China
Abstract:

Directed strongly regular graphs were introduced by Duval in 1998 as one of the possible generalization of classical strongly regular graphs to the directed case. Duval also provided several construction methods for directed strongly regular graphs. In this paper, an infinite family of directed strongly regular graphs is constructed, as generalized Cayley graphs.

Yan Guo1
1College of Traffic Engineering, Huanghe Jiaotong University, Wuzhi, Henan, 454950, China
Abstract:

Green construction is becoming a mainstream model of the transformation and upgrading of the construction industry, which has the advantages of energy saving, environmental protection and ecology, which can effectively reduce energy deficiency and improve environmental quality, which is the need for high quality sustainable development. This study is based on BIM software and the intelligent construction technology to propose the green architectural design party case. Building energy-saving efficiency evaluation system, using fuzzy Borda method and the CRITIC method of evaluation, the objective of the index, and the example of a community, the use of the object meta-effect model. The evaluation scores of the energy saving efficiency of the building of green energy saving and renovation are in the 90.11-99.28 points, and the high energy demand in the process of running the use of the building is excellent in the heating, refrigeration and other aspects of the building. This paper shows that the goal of the green transformation project is basic, which is effective and the efficiency of energy efficiency is generated. This study can provide guidance for the work of the green building energy saving and renovation work, and further promote the energy saving and transformation of China.

Zhicheng Ma1
1Songyuan Yongsheng Construction Company, Songyuan, Jilin, 138000, China
Abstract:

The supply chain applies large number according to the technology, can reduce the cost of each link, optimize the resource allocation, increase the enterprise benefit. In this paper, the supply chain cost control program based on large number according to the previous forecast, the control of the event and the analysis of the three levels of the analysis of the supply chain. The combination time series model and the multivariate regression model, the joint CPFR concept, the establishment of the CPFR sales combination demand prediction model, the design form according to the sales prediction system, the resource optimization plan of the supply chain inventory in real time. Analyze the prediction effect of the combination prediction model, predict the product sales in the week, calculate the product safety inventory and the remaining inventory. The analysis is based on the cost control effect of the enterprise supply chain according to the sales forecast. The cost of purchasing the supply chain costs less than the operating income, which fell to 0.5107in 2023. The gross margin of gross profit was 0.53666 in 2023, which was controlled by the gross margin, and the gross profit was improved. It is said that the enterprise is using large number according to the technology to the supply chain resource optimization in the supply chain cost control, the cost control effect is better.

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