A (p, q)-graph G = (V, E) is said to be (k, d)-arithmetic, where k and d are positive integers if its p vertices admits a labeling of distinct non-negative integers such that the values of the edges obtained as the sums of the labels of their end vertices form the set {k, k + d, k + 2d, ..., k + (q - 1)d}. In this paper we prove that for all odd n, the generalized web graph W (t, n) and some cycle related graphs are (k, d)-arithmetic. Also we prove that a class of trees called T<inf>p</inf>-trees and subdivision of T<inf>p</inf>-trees are (k + q - 1) (d, d)-arithmetic for all positive integers k and d.
| dc.contributor.author | Hegde, S.M. | |
| dc.contributor.author | Shetty, S. | |
| dc.date.accessioned | 2026-02-05T11:00:30Z | |
| dc.date.issued | On arithmetic graphs | |
| dc.description.abstract | 2002 | |
| dc.identifier.citation | Indian Journal of Pure and Applied Mathematics, 2002, 33, 8, pp. 1275-1283 | |
| dc.identifier.issn | 195588 | |
| dc.identifier.uri | https://idr.nitk.ac.in/handle/123456789/27996 | |
| dc.subject | Arithmetic Graphs | |
| dc.subject | Arithmetic Labelings | |
| dc.subject | Trees | |
| dc.title | A (p, q)-graph G = (V, E) is said to be (k, d)-arithmetic, where k and d are positive integers if its p vertices admits a labeling of distinct non-negative integers such that the values of the edges obtained as the sums of the labels of their end vertices form the set {k, k + d, k + 2d, ..., k + (q - 1)d}. In this paper we prove that for all odd n, the generalized web graph W (t, n) and some cycle related graphs are (k, d)-arithmetic. Also we prove that a class of trees called T<inf>p</inf>-trees and subdivision of T<inf>p</inf>-trees are (k + q - 1) (d, d)-arithmetic for all positive integers k and d. |