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Infinitely Many Trees with Maximum Number of Holes Zero, One, and Two
Joint Authors
Kola, Srinivasa Rao
Gudla, Balakrishna
Niranjan, P. K.
Source
Journal of Applied Mathematics
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-09-20
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
An L(2,1)-coloring of a simple connected graph G is an assignment f of nonnegative integers to the vertices of G such that fu-fv⩾2 if d(u,v)=1 and fu-fv⩾1 if d(u,v)=2 for all u,v∈V(G), where d(u,v) denotes the distance between u and v in G.
The span of f is the maximum color assigned by f.
The span of a graph G, denoted by λ(G), is the minimum of span over all L(2,1)-colorings on G.
An L(2,1)-coloring of G with span λ(G) is called a span coloring of G.
An L(2,1)-coloring f is said to be irreducible if there exists no L(2,1)-coloring g such that g(u)⩽f(u) for all u∈V(G) and g(v) If f is an L(2,1)-coloring with span k, then h∈0,1,2,…,k is a hole if there is no v∈V(G) such that f(v)=h. The maximum number of holes over all irreducible span colorings of G is denoted by Hλ(G). A tree T with maximum degree Δ having span Δ+1 is referred to as Type-I tree; otherwise it is Type-II. In this paper, we give a method to construct infinitely many trees with at least one hole from a one-hole tree and infinitely many two-hole trees from a two-hole tree. Also, using the method, we construct infinitely many Type-II trees with maximum number of holes one and two. Further, we give a sufficient condition for a Type-II tree with maximum number of holes zero.
American Psychological Association (APA)
Kola, Srinivasa Rao& Gudla, Balakrishna& Niranjan, P. K.. 2018. Infinitely Many Trees with Maximum Number of Holes Zero, One, and Two. Journal of Applied Mathematics،Vol. 2018, no. 2018, pp.1-14.
https://search.emarefa.net/detail/BIM-1176070
Modern Language Association (MLA)
Kola, Srinivasa Rao…[et al.]. Infinitely Many Trees with Maximum Number of Holes Zero, One, and Two. Journal of Applied Mathematics No. 2018 (2018), pp.1-14.
https://search.emarefa.net/detail/BIM-1176070
American Medical Association (AMA)
Kola, Srinivasa Rao& Gudla, Balakrishna& Niranjan, P. K.. Infinitely Many Trees with Maximum Number of Holes Zero, One, and Two. Journal of Applied Mathematics. 2018. Vol. 2018, no. 2018, pp.1-14.
https://search.emarefa.net/detail/BIM-1176070
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1176070