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Wyświetlanie 1-10 z 11
Tytuł:
Pentagonal Graceful Labeling of Some Graphs
Autorzy:
Mahendran, S.
Murugan, K.
Powiązania:
https://bibliotekanauki.pl/articles/1193373.pdf
Data publikacji:
2021
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Pentagonal graceful number
pentagonal graceful graphs
pentagonal graceful labeling
Opis:
Numbers of the form (n(3n-1))/2 for all n ≥ 1 are called pentagonal numbers. Let G be a graph with p vertices and q edges. Let f : V(G)→{0,1,2,…,P_q} where P_q is the q^th pentagonal number be an injective function. Define the function f *: E(G) → {1,5,…,P_q} such that f *(uv)=│f(u)-f(v)│for all edges uv∈E(G). If f *( E(G)) is a sequence of distinct consecutive pentagonal numbers {P_1,P_2,…,P_q}, then the function f is said to be pentagonal graceful labeling and the graph which admits such a labeling is called a pentagonal graceful graph. In this paper, pentagonal graceful labeling of some graphs is studied.
Źródło:
World Scientific News; 2021, 155; 98-112
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some Results on Octagonal Graceful Graphs
Autorzy:
Kovusalya, K.
Namasivayam, P.
Powiązania:
https://bibliotekanauki.pl/articles/1193388.pdf
Data publikacji:
2021
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Octagonal graceful number
octagonal graceful graphs
octagonal graceful labeling
Opis:
Numbers of the form On = n (3n-2) for all n≥1 are called octagonal numbers. Let G be a graph with p vertices and q edges. Let f: V (G) → {0, 1, 2… Om} where Om is the mth octagonal number be an injective function. Define the function f*:E(G) → {1,8,21,..,Om} such that f*(uv) = |f(u)-f(v)| for all edges uvϵE(G). If f*(E (G)) is a sequence of distinct consecutive octagonal numbers {O1, O2 , …, Oq }, then the function f is said to be octagonal graceful labeling and the graph which admits such a labeling is called a octagonal graceful graph. In this paper, octagonal graceful labeling of some graphs is studied.
Źródło:
World Scientific News; 2021, 156; 1-12
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Octagonal Graceful Labeling of Some Special Graphs
Autorzy:
Mahendran, S.
Powiązania:
https://bibliotekanauki.pl/articles/1193401.pdf
Data publikacji:
2021
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Octagonal graceful number
octagonal graceful graphs
octagonal graceful labeling
Opis:
Numbers of the form 3n2-2n for all n ≥ 1 are called octagonal numbers. Let G be a graph with p vertices and q edges. Let f :V(G)→{0,1,2,…,M_q} where M_q is the q^th octagonal number be an injective function. Define the function f *: E(G) → {1,8,…,M_q} such that f *(uv) = │f(u)-f(v)│for all edges uv ∈E(G). If f *(E(G)) is a sequence of distinct consecutive octagonal numbers {M_1,M_2,…,M_q}, then the function f is said to be octagonal graceful labeling and the graph which admits such a labeling is called a octagonal graceful graph. In this paper, octagonal graceful labeling of some graphs is studied.
Źródło:
World Scientific News; 2021, 156; 87-101
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some Special Graceful Labeling Results of Pentagonal Pyramidal Graceful Graphs
Autorzy:
Mahendran, S.
Powiązania:
https://bibliotekanauki.pl/articles/1193441.pdf
Data publikacji:
2021
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Pentagonal pyramidal graceful number
pentagonal pyramidal graceful graphs
pentagonal pyramidal graceful labeling
Opis:
Numbers of the form (n^(2 ) (n+1))/2 for all n≥1 are called pentagonal pyramidal numbers. Let G be a graph with p vertices and q edges. Let Ψ : V(G) →{0, 1, 2… M_r} where M_r is the r^th pentagonal pyramidal number be an injective function. Define the function Ψ*:E(G) →{1,6,18,.., M_r} such that Ψ *(uv) = |Ψ (u)- Ψ (v)| for all edges uvϵE(G). If Ψ*(E (G)) is a sequence of distinct consecutive pentagonal pyramidal numbers {M_1,M_2, …, M_r}, then the function Ψ is said to be pentagonal pyramidal graceful labeling and the graph which admits such a labeling is called a pentagonal pyramidal graceful graph. In this paper, some special graceful labeling results of pentagonal pyramidal graceful graphs is studied.
Źródło:
World Scientific News; 2021, 157; 67-79
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some Special Results for Square Pyramidal Graceful Graphs
Autorzy:
Mahendran, S.
Powiązania:
https://bibliotekanauki.pl/articles/1193411.pdf
Data publikacji:
2021
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Square pyramidal graceful number
square pyramidal graceful graphs
square pyramidal graceful labeling
Opis:
Numbers of the form (n(n+1)(2n+1))/6 for all n≥1 are called square pyramidal numbers. Let G be a graph with p vertices and q edges. Let τ : V(G) →{0, 1, 2… M_k} where M_k is the k^th square pyramidal number be an injective function. Define the function τ*:E(G)→{1,5,14,.., M_k} such that τ *(uv) = |τ (u)- τ (v)| for all edges uvϵE(G). If τ *(E(G)) is a sequence of distinct consecutive square pyramidal numbers {M_1,M_2, …, M_k}, then the function τ is said to be square pyramidal graceful labeling and the graph which admits such a labeling is called a square pyramidal graceful graph. In this paper, some special results for square pyramidal graceful graphs is studied.
Źródło:
World Scientific News; 2021, 156; 147-160
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some results on centered triangular graceful graphs
Autorzy:
Baskar, M.
Namasivayam, P.
Syed Ali Nisaya, M. P.
Mahendran, S.
Powiązania:
https://bibliotekanauki.pl/articles/1193414.pdf
Data publikacji:
2021
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Centered triangular numbers
centered triangular graceful graphs
centered triangular graceful labeling
Opis:
Let G be a graph with p vertices and q edges. The nth centered triangular number is denoted by C_n, where C_n = 1/2 (3n2 - 3n + 2). A centered triangular graceful labeling of a graph G is a one-to-one function f : V (G) → {0,1,…C_q} that induces a bijection f *: E(G) →{C_1 〖,C〗_2,…C_q} of the edges of G defined by f * (e) = │f(u) - f(v)│, for all e = uv ∊ E(G). The graph which admits such labeling is called a centered triangular graceful graph.
Źródło:
World Scientific News; 2021, 156; 176-191
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Second order triangular graceful graphs
Autorzy:
Sakthi Sankari, R.
Syed Ali Nisaya, M. P.
Powiązania:
https://bibliotekanauki.pl/articles/1193377.pdf
Data publikacji:
2021
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Second order triangular graceful graph
Second order triangular graceful labeling
Second order triangular number
Opis:
Let G=(V,E) be a graph with p vertices and q edges. A second order triangular graceful labeling of a graph G is an one to one function φ:V(G)→{0,1,2,…,B_q} where B_q is the qth second order triangular number, ie., B_q=1/6 q(q+1)(2q+1), that induces a bijection φ^*:E(G)→{B_1,B_2,…,B_q} of the edges of G defined by φ^* (uv) =|φ(u)-φ(v)| ∀ e=uv ∈E(G). A graph which admits such labeling is called a second order triangular graceful graph. In this paper, we introduce second order triangular graceful labeling and we prove that star, subdivision of star, nK_1,3, nK_2, bistar, path, comb, coconut tree, shrub and Y-tree are second order triangular graceful graphs.
Źródło:
World Scientific News; 2021, 155; 140-154
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the Beta-Number of Forests with Isomorphic Components
Autorzy:
Ichishima, Rikio
López, Susana-Clara
Muntaner-Batle, Francesc Antoni
Oshima, Akito
Powiązania:
https://bibliotekanauki.pl/articles/31342282.pdf
Data publikacji:
2018-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
beta-number
strong beta-number
graceful labeling
Skolem sequence
hooked Skolem sequence
Opis:
The beta-number, β(G), of a graph G is defined to be either the smallest positive integer n for which there exists an injective function f : V (G) → {0, 1, ..., n} such that each uv ∈ E (G) is labeled |f (u) − f (v)| and the resulting set of edge labels is {c, c+1, ..., c+|E(G)|−1} for some positive integer c or +∞ if there exists no such integer n. If c = 1, then the resulting beta-number is called the strong beta-number of G and is denoted by βs (G). In this paper, we show that if G is a bipartite graph and m is odd, then β (mG) ≤ mβ (G) + m − 1. This leads us to conclude that β (mG) = m|V(G)|−1 if G has the additional property that G is a graceful nontrivial tree. In addition to these, we examine the (strong) beta-number of forests whose components are isomorphic to either paths or stars.
Źródło:
Discussiones Mathematicae Graph Theory; 2018, 38, 3; 683-701
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Higher order triangular graceful labeling of some graphs
Autorzy:
Sakthi Sankari, R.
Syed Ali Nisaya, M. P.
Powiązania:
https://bibliotekanauki.pl/articles/1193398.pdf
Data publikacji:
2021
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
fifth order
fifth order triangular graceful graph
fifth order triangular graceful labeling
fifth order triangular numbers
fourth order
third order
Opis:
A (p, q) graph G is said to admit higher order triangular graceful labeling if its vertices can be labeled by the integers from 0 to qth higher order triangular numbers such that the induced edge labels obtained by the absolute difference of the labels of end vertices are the first q higher order triangular numbers. A graph G which admits higher order triangular graceful labeling is called a higher order triangular graceful graph. In this paper, third order, fourth order, fifth order triangular graceful labeling are introduced and third order, fourth order, fifth order triangular graceful labeling of star graph, subdivision of star, nK_2, path, comb, bistar, coconut tree, nK_1,3 are studied.
Źródło:
World Scientific News; 2021, 156; 40-61
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the Number of α-Labeled Graphs
Autorzy:
Barrientos, Christian
Minion, Sarah
Powiązania:
https://bibliotekanauki.pl/articles/31342431.pdf
Data publikacji:
2018-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
α -labeling
α -graph
graceful triangle
Opis:
When a graceful labeling of a bipartite graph places the smaller labels in one of the stable sets of the graph, it becomes an α-labeling. This is the most restrictive type of difference-vertex labeling and it is located at the very core of this research area. Here we use an extension of the adjacency matrix to count and classify α-labeled graphs according to their size, order, and boundary value.
Źródło:
Discussiones Mathematicae Graph Theory; 2018, 38, 1; 177-188
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-10 z 11

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