On (2-d)-Kernels in the Tensor Product of Graphs

Paweł Bednarz

doi:10.3390/sym13020230

Abstract

In this paper, we study the existence, construction and number of (2-d)-kernels in the tensor product of paths, cycles and complete graphs. The symmetric distribution of (2-d)-kernels in these products helps us to characterize them. Among others, we show that the existence of (2-d)-kernels in the tensor product does not require the existence of a (2-d)-kernel in their factors. Moreover, we determine the number of (2-d)-kernels in the tensor product of certain factors using Padovan and Perrin numbers.

Highlights

Introduction and Preliminary ResultsIn general, we use the standard terminology and notation of graph theory; see [1]
This paper considers the problem of the existence of (2-d)-kernels and their number in the tensor product of graphs
We present results concerning the existence problems of (2-d)-kernels, as well as their number in the tensor product of paths, cycles and complete graphs

Summary

Introduction

Introduction and Preliminary ResultsIn general, we use the standard terminology and notation of graph theory; see [1]. This paper considers the problem of the existence of (2-d)-kernels and their number in the tensor product of graphs. The problem of counting various sets (dominating, independent, kernels) in graphs and their relations to the numbers of the Fibonacci type were studied in [11,24,28].

Results

Conclusion