Jacobsthal numbers in generalised Petersen graphs
نویسندگان
چکیده
منابع مشابه
Jacobsthal numbers in generalised Petersen graphs
We prove that the number of 1-factorisations of a generalised Petersen graph of the type GP (3k, k) is equal to the kth Jacobsthal number J(k) if k is odd, and equal to 4J(k), when k is even. Moreover, we verify the list colouring conjecture for GP (3k, k).
متن کاملGraceful labellings for an infinite class of generalised Petersen graphs
We exhibit a graceful labelling for each generalised Petersen graph P8t,3 with t ≥ 1. As an easy consequence, we obtain that for any fixed t the corresponding graph is the unique starter graph for a cyclic edgedecomposition of the complete graph K2t+1. Due to its extreme versatility, the technique employed looks promising for finding new graceful labellings, not necessarily involving generalise...
متن کاملNew families of Jacobsthal and Jacobsthal-Lucas numbers
In this paper we present new families of sequences that generalize the Jacobsthal and the Jacobsthal-Lucas numbers and establish some identities. We also give a generating function for a particular case of the sequences presented. Introduction Several sequences of positive integers were and still are object of study for many researchers. Examples of these sequences are the well known Fibonacci ...
متن کاملOn the crossing numbers of certain generalized Petersen graphs
McQuillan, D. and R.B. Richter, On the crossing numbers of certain generalized Petersen graphs, Discrete Mathematics 104 (1992) 311-320. In his paper on the crossing numbers of generalized Petersen graphs, Fiorini proves that P(8, 3) has crossing number 4 and claims at the end that P(10, 3) also has crossing number 4. In this article, we give a short proof of the first claim and show that the s...
متن کاملDistinguishing and Distinguishing Chromatic Numbers of Generalized Petersen Graphs
Albertson and Collins defined the distinguishing number of a graph to be the smallest number of colors needed to color its vertices so that the coloring is preserved only by the identity automorphism. Collins and Trenk followed by defining the distinguishing chromatic number of a graph to be the smallest size of a coloring that is both proper and distinguishing. We show that, with two exception...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Electronic Notes in Discrete Mathematics
سال: 2015
ISSN: 1571-0653
DOI: 10.1016/j.endm.2015.06.065