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Distance spectra of neighbourhood corona of graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 27 مرداد 1404 اصل مقاله (639.24 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30329.2417 | ||
| نویسندگان | ||
| K.D. Arathy* 1، 2؛ K. Pravas3 | ||
| 1Department of Mathematics, Sree Narayana College, Nattika, Kerala-680566, India | ||
| 2St. Joseph’s College (Autonomous) Irinjalakuda, Kerala-680121, Affiliated to University of Calicut, India | ||
| 3Department of Mathematics, Maharaja’s College, (Government Autonomous) Ernakulam, Kerala-682011, India | ||
| چکیده | ||
| The neighbourhood corona $G \star H$ of two graphs $G$ and $H$ is obtained by taking one copy of $G$ and $|V(G)|$ copies of $H$ and making all the neighbours of the $i^{\text{th}}$ vertex of $G$ adjacent with all the vertices in the $i^{\text{th}}$ copy of $H$. In this paper we describe the distance eigenvalues and corresponding eigenvectors of $G \star H$ in terms of the adjacency spectrum of $G$ and $H$ when $G$ is a regular triangle-free graph with diameter 2 and $H$ is regular. Several constructions are proposed using line graphs, iterated line graphs, double graphs, strong double graphs and complement graphs to obtain infinitely many distance non-cospectral pairs of distance equienergetic graphs and non-isomorphic pairs of distance cospectral graphs. Also we obtain the distance Laplacian spectrum of $G \star H$ in terms of the distance Laplacian spectrum of $G$ and Laplacian spectrum of $H$ when $G$ is a transmission regular triangle-free graph with diameter 2. Further we find the distance signless Laplacian spectrum of $G \star H$ in terms of the distance signless Laplacian spectrum of $G$ and signless Laplacian spectrum of $H$ when $G$ is a transmission regular triangle-free graph with diameter 2 and $H$ is regular. We also construct infinitely many non-isomorphic pairs of distance Laplacian cospectral graphs and distance signless Laplacian cospectral graphs. | ||
| کلیدواژهها | ||
| Distance spectrum؛ distance Laplacian spectrum؛ distance signless Laplacian spectrum؛ distance equienergetic graphs؛ distance cospectral graphs | ||
| مراجع | ||
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