Work

A Complete Characterisation of Half-Sunlet Decompositions of Line Graphs of Complete Graphs

Year: 2026

Type: article

Abstract: Let L(Kn) be the line graph of Kn and let HS6 be the graph obtained from a 4-cycle by attaching a pendant edge at each of two antipodal vertices. We prove that L(Kn) has an HS6-decomposition if and only if n≥4 and n≢3(mod4). The proof splits L(Kn) into smaller line graphs together with graphs W(m,k) built from k triangle bundles glued along shared degree-two vertices, characterises the single-copy case, and handles W(m,2) via a construction attached to each cycle of a cycle decomposition of Km.

Source: AppliedMath

DOI: 10.3390/appliedmath6110192

Authors: Gajendran Palaniyandi, Aramuthakannan Soundararajan, Sandhya Soundararajan

Institutions: PSG INSTITUTE OF TECHNOLOGY AND APPLIED RESEARCH, ICFAI Business School

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,207

OpenAlex ID: W7225784781

FWCI:

Cites: 18

Cited by:

Related to: