### ON THE SIGNED MATCHINGS OF GRAPHS

Samane Javan, Hamid Reza Maimani

DOI Number
https://doi.org/10.22190/FUMI2002541J
First page
541
Last page
547

#### Abstract

For a graph $G$ and any $v\in V(G)$, $E_{G}(v)$ is the set of all edges incident with $v$. A function $f:E(G)\rightarrow \{-1,1\}$ is called a
signed matching  of $G$ if  $\sum_{e\in E(v)}f(e) \leq 1$ for every ${v\in V(G)}$. For a signed matching $x$, set $x(E(G))=\sum_{e\in E(G))}x(e)$. The signed  matching number of $G$, denoted by $\beta_1'(G)$, is the maximum $x(E(G))$ where the maximum is taken over all signed matching over $G$. In this paper we obtain the signed matching number of some families of graphs and study the signed matching number of subdivision and edge deletion of edges of graph.

#### Keywords

signed matching; signed matching number; bipartite graphs

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#### References

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DOI: https://doi.org/10.22190/FUMI2002541J

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