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On Connected Bipartite $Q$-Integral Graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 16 بهمن 1402 اصل مقاله (798.63 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.29215.1895 | ||
| نویسندگان | ||
| Jesmina Pervin1؛ Lavanya Selvaganesh* 2 | ||
| 1Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, UP, India | ||
| 2Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, UP, India | ||
| چکیده | ||
| A graph $G$ is said to be $H$-free if $G$ does not contain $H$ as an induced subgraph. Let $\mathcal{S}_{n}^2(m)$ be a \textit{variation of double star $\mathcal{S}_{n}^2$} obtained by adding m (<=n) disjoint edges between the pendant vertices which are at distance 3 in $\mathcal{S}_{n}^2$. A graph having integer eigenvalues for its signless Laplacian matrix is known as a Q-integral graph. The Q-spectral radius of a graph is the largest eigenvalue of its signless Laplacian. Any connected Q-integral graph G with Q-spectral radius 7 and maximum edge-degree 8 is either $K_{1,4}\square K_2$ or contains $\mathcal{S}_{4}^2(0)$ as an induced subgraph or is a bipartite graph having at least one of the induced subgraphs $\mathcal{S}_{4}^2(m)$, (m=1, 2, 3). In this article, we improve this result by showing that every connected Q-integral graph G having Q-spectral radius 7, maximum edge-degree 8 is always bipartite and $\mathcal{S}_{4}^2(3)$-free. | ||
| کلیدواژه‌ها | ||
| Edge-degree؛ H-free graph؛ Signless Laplacian matrix؛ Q-integral graph | ||
| مراجع | ||
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