We introduce three new twoparameter generalizations of Fibonacci numbers. These generalizations are closely related to
In general we use the standard terminology of the combinatorics and graph theory; see [
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In this paper we introduce three new twoparameter generalizations of distance Fibonacci numbers. They are closely related with the numbers
Let
If
Table
Distance

















































































Let
In Table
Distance

















































































Let
Table
Distance

















































































By the definition of distance
In this section we present some combinatorial and graph interpretations of distance
if
Let
Let
for each
for each
Assume that the condition (c2) is satisfied. Then the subfamily
Assume that the condition (c3) is satisfied. Then the subfamily
Let
Let
Let
Analogously as Theorem
Let
Let
Distance
Among
Consider a multipath
Let
The number
Let
Let
Consider a multipath
Let
Then we can choose the edge
Proving analogously as in case (
Consequently
Analogously we can prove combinatorial interpretations of numbers
In this section we give some identities and some relations between distance
For
We give the proof for distance
For
For
For
For
Analogously we can prove the following.
For
For
The author declares that there is no conflict of interests regarding the publication of this paper.
The author would like to thank the referee for helpful comments and suggestions for improving an earlier version of this paper.