Dense Graph Homomorphisms of Co spectral Rigid Circuit Graphs are Cycle Decompositions - Dr. P. JAYALAKSHMI,; T. RENUGA,; S. ANITHA, (Utilitas Mathematica, 2025)
Understanding the structure of graphs is essential for progress in various areas of graph theory and its applications. This paper focuses on a specific structural property across multiple classes of graphs. Graphs containing a clique of size r(i.e., Kr-cospectralchordal dense graphs) are particularly significant in external graph theory. While many results have been established regarding dense triangle-free graphs, less is known about dense Kr-cospectralchordal dense graphs for r  4. The conditions required to decompose the entire graph of odd order into cycles of a fixed even length and the complete graph of even order minus 1-factor into cycles of a fixed odd length are also demonstrated to be sufficient. This paper highlights key findings related to cores, homomorphisms and cycle decomposition.