There are various engineering applications dealing with the prototype problem of finding the best p-medians in a weighted GRAPH. However, the heuristic developments are still of concern due to their complexity. This paper utilizes genetic algorithm as a well-known reliable evolutionary search for such a purpose. Problem formulation is studied, introducing a characteristic GRAPH and specialized genotype representation called\Direct Index Coding". The genetic operators are also modified due to problem requirements, and further tuned using a simulated annealing approach. Such an enhanced evolutionary search tool is then applied to a number of examples to show its effectiveness regarding the exact results, and to compare efficiency between tuned and non-tuned GA.

With the increasing interconnectedness of communications and social networks, GRAPH-based learning techniques offer valuable information extraction from data. Traditional centralized learning methods faced challenges, including data privacy violations and costly maintenance in a centralized environment. To address these, decentralized learning approaches like Federated Learning have emerged. This study explores the significant attention Federated Learning has gained in GRAPH classification and investigates how Model Agnostic Meta-Learning (MAML) can improve its performance, especially concerning non-IID (Non-Independent Identically Distributed) data distributions.In real-world scenarios, deploying Federated Learning poses challenges, particularly in tuning client parameters and structures due to data isolation and diversity. To address this issue, this study proposes an innovative approach using Genetic ALGORITHMS (GA) for automatic tuning of structures and parameters. By integrating GA with MAML-based clients in Federated Learning, various aspects, such as GRAPH classification structure, learning rate, and optimization function type, can be automatically adjusted. This novel approach yields improved accuracy in decentralized learning at both the client and server levels.

Community detection is one of the important topics regarding complex network study. There are many community detection ALGORITHMS such as Streaming Community Detection Algorithm (SCoDA) and Order Statistics Local Optimization Method (OSLOM). However, the performance of these ALGORITHMS, in overlap communities and communities with ambiguous structure, is problematic. In community detection ALGORITHMS achieving accurate results is a challenge. In this paper, we’ ve proposed a method based on finding maximal cliques and generating the corresponding GRAPH in order to use as an input to SCoDA and OSLOM ALGORITHMS. Synthetic non-overlap and overlap GRAPHs and real GRAPHs data are used in our experiments. F1score and NM1 score functions are utilized as our evaluation criteria. We have shown that the improved version of SCoDA demonstrated better results in comparison to the original SCoDA algorithm, and the improved version of OSLOM was also superior in performance when compared with the original OSLOM algorithm.

The independence GRAPH Ind(G) of a GRAPH G is the GRAPH with vertices as maximum independent sets of G and two vertices are adjacent, if and only if the corresponding maximum independent sets are disjoint. In this work, we find the independence GRAPH of Cartesian product of d copies of complete GRAPHs Kq, which is known as the Hamming GRAPH H(d, q). Greenwell and Lovasz [7] found that the independence number of direct product of d copies of Kq as qd−1. We prove that the independence number of Hamming GRAPH H(d, q), which is cartesian product of d copies of Kq, is also qd−1. As an application of our findings, we find answers for rook problem in higher dimensional square chess board.

GRAPHs are common data structures which widely used for information storage and retrieval. Occasionally some vertices of a GRAPH contain specific features or information, which we value in their effect. We consider modeling this effect formally, and we devise two super-fast ALGORITHMS to approximate the colored average degree. In the first method, we assume the information of each vertex is available; hence, the provided algorithm works with a 2+ϵ approximation factor. Eventually, we waive this assumption and find another algorithm with the same approximation factor, which computes the answer in the sublinear expected time.

In this paper, we find the star chromatic number of central GRAPH of complete bipartite GRAPH and corona GRAPH of complete GRAPH with path and cycle.

Let R be a commutative ring and M be an R-module. The M-intersection GRAPH of ideals of R, denoted by GM(R) is a GRAPH with the vertex set I(R) ∗, , and two distinct vertices I and J are adjacent if and only if IM ∩,JM ̸, = 0. In this paper, we study GR/J (R/I), where I and J are ideals of R and I ⊆,J. We characterize all ideals I and J for which GR/J (R/I) is planar, outerplanar or ring GRAPH.