CONVEX NEIGHBORHOOD POLYNOMIAL OF GRAPHS

被引：0

作者：

Abdurasid, Sonny C. ^{[1
]}

Amiruddin, Bayah J. ^{[2
]}

Salim, Jeffrey Imer C. ^{[2
]}

Artes Jr, Rosalio G. ^{[2
]}

机构：

[1] Mindanao State Univ, Sci High Sch, Tawi Tawi Coll Technol & Oceanog, Inst Oceanog & Environm Sci, Bongao 7500, Tawi Tawi, Philippines

[2] Mindanao State Univ, Math & Sci Dept, Coll Arts & Sci, Tawi Tawi Coll Technol & Oceanog, Bongao 7500, Tawi Tawi, Philippines

来源：

ADVANCES AND APPLICATIONS IN DISCRETE MATHEMATICS | 2023年 / 40卷 / 01期

关键词：

convex set1; neighborhood system; convex neighborhood polynomial;

D O I：

10.17654/0974165823061

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The idea of polynomial representation describing a graph using a specified substructure with a corresponding neighborhood system was first introduced by Artes et al. [20] by considering the common neighborhood systems of cliques in a graph. In this paper, we introduce the notion of a convex neighborhood polynomial for a graph and establish some of its properties. Moreover, we investigate the convex neighborhood polynomials of some special graphs such as paths, cycles, complete graphs, and complete bipartite graphs. More interestingly, we have shown that the convex neighborhood polynomial of a path can be expressed as a linear combination of the elements of {1, f(x), f '(x)} for some nth partial sum f(x) of a geometric series.

引用

页码：125 / 137

页数：13

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