ABSTRACT

A $signedgraph$ is a graph whose edges carry the weight ‘+’ or ‘−’. A signed graph S is called sign-regular if $d^{-}\left(v\right)$ is same for all $v\in V$ and $d^{+}\left(v\right)$ is same for all $v\in V$. The problems of embedding $(i,j)$-sign-regular signed graphs in $(i+k,j+l)$-sign-regular signed graphs is one of the fascinating problem from application point of view which is dealt in this paper with insertion of least number of vertices in S and the problem of finding least number of non-isomorphic co-regular signed graphs is explored. We also define the relationship between characteristic polynomial of graph G and the graph in which it embeds.

摘要

一种$s\mathrm{一世}GnedGr\mathrm{一种}pH$是一个图，其边的权重为“+”或“-”。有符号图S称为正则符号，如果$d^{-}\left(v\right)$所有人都一样$v\in 五$和$d^{+}\left(v\right)$所有人都一样$v\in 五$. 嵌入问题$(\mathrm{一世},j)$-sign-正则有符号图$(\mathrm{一世}+ķ,j+l)$-sign-regular signed graphs 从应用的角度来看是一个引人入胜的问题之一，本文通过在S中插入最少数量的顶点来处理，并探讨了找到最少数量的非同构共正则签名图的问题. 我们还定义了图G的特征多项式与其嵌入的图之间的关系。