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Edge-Vertex Dominating Sets and Edge-Vertex Domination Polynomials of Cycles
| Content Provider | Semantic Scholar |
|---|---|
| Copyright Year | 2015 |
| Abstract | Let G = (V, E) be a simple graph. A set S ⊆ E(G) is an edge-vertex dominating set of G (or simply an ev-dominating set), if for all vertices v ∈ V(G); there exists an edge e∈S such that e dominates v. Let ( ) ev n D C i , denote the family of all ev-dominating sets of n C with cardinality i. Let ( ) ( ) ev n ev n d C i D C i , , = . In this paper, we obtain a recursive formula for ( ) ev n d C i , . Using this recursive formula, we construct the polynomial, ( ) ( ) ∑ i ev n ev n n i D C x d C i x 4 , , = = , which we call edgevertex domination polynomial of n C (or simply an ev-domination polynomial of n C ) and obtain some properties of this polynomial. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://file.scirp.org/pdf/OJDM_2015093011143843.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Cardinality Dominating set Epidermodysplasia Verruciformis Graph (discrete mathematics) Graph - visual representation Polynomial Recursion Vertex electronvolt |
| Content Type | Text |
| Resource Type | Article |
