Aug 2026· Discrete Mathematics, Algorithms and Applications (DMAA)· 0 citations
Abstract
The notion of graph complements has been widely generalized to study diverse structural and spectral properties of graphs. In this paper, we introduce and investigate the concept of generalized color complements of graphs with respect to a prescribed vertex partition. Building on earlier work on generalized color complements, we focus on structural properties arising from the interaction between graph coloring and partition-based complement operations. Sufficient conditions are established under which generalized color complements are disconnected, regular, and Eulerian. Explicit expressions are derived for the degree of any vertex in the generalized color complements [Formula: see text], [Formula: see text]. Furthermore, several classes of self-color-complementary graphs are identified for fixed partitions. A collection of illustrative examples is provided to demonstrate and validate the theoretical results. The findings extend existing results on generalized complements to a color-based framework and contribute to a deeper understanding of partition-dependent graph complements.
This thesis investigates two central directions in algebraic graph theory, with an emphasis on spectral methods: spectral determination of graphs and transitivity properties of generalized-Hamming graphs and their complements. The first part focuses on graphs that are determined by the spectra of associated matrices. W...
The locating-chromatic number of a graph combines proper vertex coloring with vertex identification through distances to color classes. Although this parameter has been studied for many graph families, general results for bipartite graphs remain limited. Bipartite graphs contain structural symmetries, especially within...
Dian Kastika Syofyan, E. Baskoro, H. Assiyatun et al.· Baghdad Science Journal· 0 citations
Identifying and constructing graphs that are determined by their generalized spectrum (DGS) is a significant and challenging problem in spectral graph theory. Recently, a simple criterion for almost controllable graphs to be DGS was proposed by Lin et al. (2026), utilizing the modified walk matrix. In this paper, we in...
This study explores the spectral characteristics and energy distributions associated with selected graph operations derived from the first Zagreb, second Zagreb, and sum-connectivity matrices to contribute to understanding how algebraic operations induce spectral energy shifts analogous to perturbations in physical or...
S. Sripriya, A. Anuradha· Baghdad Science Journal· 0 citations
In this paper, we construct a class of infinite graphs, called substitution graphs. The vertex set consists of all finite words over a finite alphabet. A directed graph is formed by adding vertical edges connecting each word to its children and horizontal edges defined recursively by two finite directed graphs G and J:...
Qing-Cheng Zeng, Cheng Zeng, Yu-Mei Xue et al.· 0 citations
Hypergraphs extend classical graphs by allowing hyperedges to connect any nonempty subset of vertices, thereby capturing complex group-level relationships. Superhypergraphs advance this framework by introducing recursively nested powerset layers, enabling the representation of hierarchical and self-referential links am...
Unknown authors· Indonesian Journal of Combin...· 0 citations
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