The Mostar and Wiener index of alternate Lucas cubes

Document Type : Research Paper


1 Department of Computer Science, University of California Santa Barbara, CA 93106, USA

2 Department of Mathematics and Science Education, Hacettepe University, 06800, Ankara, Turkey

3 Department of Mathematics, TOBB University of Economics and Technology, 06560, Ankara, Turkey


The Wiener index and the Mostar index quantify two distance related properties of connected graphs: the Wiener index is the sum of the distances over all pairs of vertices and the Mostar index is a measure of how far the graph is from being distance-balanced. These two measures have been considered for a number of interesting families of graphs. In this paper, we determine the Wiener index and the Mostar index of alternate Lucas cubes. Alternate Lucas cubes form a family of interconnection networks whose recursive construction mimics the construction of the well-known Fibonacci cubes.


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