Subspace-based subspace sum graph on vector spaces

doi:10.1007/s00500-021-06006-7

2021-08-03

PRE

Ashraf, Mohammad

Mohit Kumar *

Aisha Jabeen

DOI：10.1007/s00500-021-06006-7

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摘要

En 中文

Suppose that V is a n-dimensional vector space and W is its fixed k-dimensional subspace such that n - k = 1. In the present article, we initiate the study of a new graph structure subspace-based subspace sum graph G(W)(V), where the vertex set V(G(W)(V)) is the collection of all subspaces W of V such that W + W not equal V and W not subset of W, i.e., V(G(W)(V)) = {W subset of V vertical bar W + W not equal V, W not subset of W} and any two distinct vertices W-1 and W-1 of G(W)(V) are adjacent if and only if W-1 + W-2 + W = V. The girth, diameter, domination number, clique number, chromatic number and maximal independent sets of G(W)(V) have been studied. It is proved that two subspace-based subspace sum graphs G(W1)(V) and G(W2)(V) are isomorphic if and only if W-1 and W-2 are isomorphic. Further, we show that G(W)(V) is weakly perfect and characterize all vector spaces V and subspaces W of V for which G(W)(V) is perfect. Finally, in case of finite field degree of a given vertex, order and size of G(W)(V) have also been obtained.

Keyword:

Diameter

Connected graph

Domination

Subspace

期刊

Soft Computing

IF:

2.5

论文数:

1.0W

被引数:

2.1W

机构

Jamia Millia Islamia

学者数:

3.8K

论文数: 3.5K

被引数: 5.3K

aligarh muslim university

学者数:

5.6K

论文数: 5.2K

被引数: 4

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