Keywords
Graph Theory, Edge Covers, Combinatorics, Integer Sequences, Recursion
Disciplines
Mathematics | Physical Sciences and Mathematics
Advisor
Feryal Alayont
Abstract
A graph is a mathematical structure consisting of vertices, representing objects, and edges that connect pairs of vertices, representing relationships between objects. When a specific graph structure can be extended in a consistent pattern we get a graph family, such as the families of path and cycle graphs. An edge cover of a graph is a subset of the graph's edges chosen so that each vertex is an endpoint of at least one edge in this subset. The edge cover counts of certain graph families, such as the path and cycle graphs, correspond to known sequences, the Fibonacci and Lucas numbers, respectively. This allows us to obtain new combinatorial interpretations of known sequences or to generate new sequences from edge covers. In this paper, we present the sequences formed by counting the total number of edge covers in graph families created by joining cycle graphs to path graphs, including the tadpole and kayak paddle graphs.
ScholarWorks Citation
Kennedy, Rowan, "Edge Covers of Joined Cycle and Path Graphs" (2023). Undergraduate Research. 7.
https://scholarworks.gvsu.edu/mathundergrad/7