Jul 2026· Advances and Applications in Discrete Mathematics· Vol 43, pp. 825-843· 0 citations
Abstract
We study the set-cordiality index of graphs, a set-valued labeling parameter introduced by Naduvath [7], and develop a general framework for bipartite graphs. A universal lower bound is established in terms of the larger partite class, along with a sufficient condition for its attainment using three consecutive layers of the Boolean lattice. To handle cases beyond this criterion, we introduce a hypercube subgraph principle, which links set-cordial labelings to graph embeddings in hypercubes. As applications, we determine exact set-cordiality indices for ladder graphs and even prism graphs, and a couple of additional results by direct arguments rather than the established principle. The results highlight the role of Boolean layer capacities and embedding structures, and we conclude with conjectures for trees and Cartesian product graphs.
Linear hypergraph set-indexers (LHSIs) associate a graph with a vertex hypergraph and an induced edge hypergraph through injective set-valuations and symmetric-difference edge labels. This study examines structural properties of graphs under LHSIs, with particular emphasis on conditions under which the associated verte...
Viji Paul, Saneesh Babu· Asian Research Journal of Ma...· 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
Conlon and Lee asked for strongly dominating graphs beyond norming graphs and even paths. We construct a two-parameter family of pairwise non-isomorphic $2$-connected strongly dominating graphs that are not seminorming, and hence lie outside the two classes of examples previously identified for signed strong domination...
For a graph and a graph family , let denote the maximum number of copies of in an ‐free ‐vertex graph. Let . Bai, Tompkins, and Well conjectured that is attained if and each block of the graph is a . In this paper, we determine the exact value of and the extremal graphs for all . The novelty of our proof is to give a...
Xiaojun Zhao, Yuejian Peng· Journal of Graph Theory· 2 citations
We introduce and study a new family of circulant digraphs associated with the cyclic group \({\mathbb Z}_N\), obtained by restricting admissible combinations of two generators \(a\) and \(b\) to three coordinate sectors. The resulting distance-like function differs from the standard directed distance in circulant digra...
C. Dalf'o, M. Fiol, M. Reyes· Utilitas mathematica· 0 citations
