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Besharati, Nazli, Emadi, Azam Sadat, Masoumi, Iman. (1405). Edge Coalitions in Graphs. , (), -. doi: 10.22108/toc.2026.150035.2385
Nazli Besharati; Azam Sadat Emadi; Iman Masoumi. "Edge Coalitions in Graphs". , , , 1405, -. doi: 10.22108/toc.2026.150035.2385
Besharati, Nazli, Emadi, Azam Sadat, Masoumi, Iman. (1405). 'Edge Coalitions in Graphs', , (), pp. -. doi: 10.22108/toc.2026.150035.2385
Besharati, Nazli, Emadi, Azam Sadat, Masoumi, Iman. Edge Coalitions in Graphs. , 1405; (): -. doi: 10.22108/toc.2026.150035.2385

Edge Coalitions in Graphs

Transactions on Combinatorics
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 07 آبان 1405
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2026.150035.2385
نویسندگان
Nazli Besharati* 1؛ Azam Sadat Emadi2؛ Iman Masoumi3
1Department of Mathematics, Faculty of Sciences Payame Noor University, Tehran, Iran
2Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
3Department of Mathematics, Faculty of Mathematical Sciences, University of Tafresh, Tafresh, Iran
چکیده
Coalition theory for vertex sets has been extensively studied, whereas

its edge counterpart has received much less attention. In this paper,

we introduce edge coalitions, edge coalition partitions, the edge

coalition number, and edge coalition graphs. We prove that every graph

with at least one edge admits an edge coalition partition and establish

bounds on the edge coalition number, including lower bounds for complete

and complete bipartite graphs. We characterize trees and unicyclic graphs

$G$ satisfying $EC(G)=|E(G)|$. For connected graphs that are neither

trees nor unicyclic, we reduce the problem to a line-graph condition;

a direct structural characterization in terms of $G$ remains open.

We also determine the edge coalition number for several standard graph

families, including paths, cycles, stars, and complete graphs of small

order. In addition, we establish structural properties of edge coalition graphs and

characterize all connected self-edge coalition graphs. These results extend

coalition theory from vertices to edges and provide a foundation for

further study of edge coalition structures.
کلیدواژه‌ها
Edge coalition؛ edge coalition partition؛ edge coalition number؛ edge coalition graph؛ edge dominating sets
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