### On b-edge consecutive edge labeling of some regular tree

Kiki Ariyanti Sugeng, Denny R. Silaban
2020 Indonesian Journal of Combinatorics
<div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span>Let </span><span>G </span><span>= (</span><span>V, E</span><span>) </span><span>be a finite (non-empty), simple, connected and undirected graph, where </span><span>V </span><span>and </span><span>E </span><span>are the sets of vertices and edges of </span><span>G</span><span>. An edge magic total labeling is a bijection </span><span>α </span><span>from </span><span>V </span><span>∪ </span><span>E
more » ... pan>E </span><span>to the integers </span><span>1</span><span>, </span><span>2</span><span>, . . . , n </span><span>+ </span>e<span>, with the property that for every </span><span>xy </span><span>∈ </span>E<span>, </span><span>α</span><span>(</span>x<span>) + </span><span>α</span><span>(</span>y<span>) + </span><span>α</span><span>(</span>xy<span>) = </span>k<span>, for some constant </span>k<span>. Such a labeling is called a </span>b<span>-edge consecutive edge magic total if </span><span>α</span><span>(</span>E<span>) = </span><span>{</span><span>b </span><span>+ 1</span><span>, b </span><span>+ 2</span><span>, . . . , b </span><span>+ </span>e<span>}</span><span>. In this paper, we proved that several classes of regular trees, such as regular caterpillars, regular firecrackers, regular caterpillar-like trees, regular path-like trees, and regular banana trees, have a </span>b<span>-edge consecutive edge magic labeling for some </span><span>0 </span><span>&lt; b &lt; </span><span>|</span><span>V </span><span>|</span><span>.</span></p></div></div></div>