On the super edge-magicness of graphs with a specific degree sequence

TL;DR

This paper investigates the conditions under which graphs with a specific degree sequence are super edge-magic, focusing on graphs of order n with degree sequence starting with 4 followed by all 2s, and explores related graph families.

Contribution

It characterizes super edge-magic graphs with a particular degree sequence and examines properties of certain graph families, proposing open problems for future research.

Findings

Identifies conditions for super edge-magicness in graphs with degree sequence 4, 2, 2, ..., 2.

Analyzes super edge-magic properties of specific graph families.

Proposes open problems related to super edge-magic graphs.

Abstract

A graph $G$ is said to be super edge-magic if there exists a bijective function $f:V\left(G\right) \cup E\left(G\right)\rightarrow \left\{1, 2, \ldots , \left\vert V\left( G\right) \right\vert +\left\vert E\left( G\right) \right\vert \right\}$ such that $f\left(V \left(G\right)\right) =\left\{1, 2, \ldots , \left\vert V\left( G\right) \right\vert \right\}$ and $f\left(u\right) + f\left(v\right) + f\left(uv\right)$ is a constant for each $uv\in E\left( G\right) $. In this paper, we study the super edge-magicness of graphs of order $n$ with degree sequence $s:4, 2, 2, \ldots, 2$. We also investigate the super edge-magic properties of certain families of graphs. This leads us to propose some open problems.