Onk-Distance Pell Numbers in 3-Edge-Coloured Graphs

Abstract

We define in this paper new distance generalizations of the Pell numbers and the companion Pell numbers. We give a graph interpretation of these numbers with respect to a special 3-edge colouring of the graph.

Extremal Trees with respect to Number of(A,B,2C)-Edge Colourings

“…, . This type of edge colouring of graph generalizes the edge colouring introduced by Piejko and Włoch in [10] and the edge colouring by monochromatic paths introduced by Trojnar-Spelina and Włoch in [13]. Many interesting results concerning some special kinds of ( 1 1 , 2 2 , .…”

“…Let ( ) be the number of all ( , , 2 )-edge colourings of the graph . The following result was given in [10].…”

“…It is well-known that (P ) = and (P ∘ K 1 ) = +1 , for ≥ 1, where P is an -vertex path, K is an -vertex complete graph, and ∘ denotes the corona of two graphs. The numbers of the Fibonacci type in the graph theory were studied intensively also in [3][4][5][6][7][8][9][10][11][12][13][14][15].…”

On Coding by (2,q)-Distance Fibonacci Numbers

“…Many mathematicians, working primarily in the field of combinatorics and discrete mathematics, began to deal with the other sequences which are a similar generalization of the Fibonacci sequence (see [34,[37][38][39][40][41][42][43][44][45]). In [34], the authors noted that from recurrence relation (13) of the sequence (F 2 (q, n)) n≥0 immediately follows that:…”

On a New One Parameter Generalization of Pell Numbers

“…In [6] there was presented k-distance Pell sequence defined as follows: P k (n) = 2P k (n − 1) + P k (n − k) for n ≥ k with P k (0) = 0, P k (n) = 2 n−1 for n = 1, 2, . .…”