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    Wyświetlanie 1-11 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 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 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 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
    Tytuł:
    Radio Graceful Hamming Graphs
    Autorzy:
    Niedzialomski, Amanda
    Powiązania:
    https://bibliotekanauki.pl/articles/31340550.pdf
    Data publikacji:
    2016-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    radio labeling
    radio graceful graph
    Hamming graph
    Opis:
    For $ k \in \mathbb{Z}_+ $ and $G$ a simple, connected graph, a $k$-radio labeling $ f : V (G) \rightarrow \mathbb{Z}_+ $ of $G$ requires all pairs of distinct vertices $u$ and $v$ to satisfy $ |f(u) − f(v)| \ge k + 1 − d(u, v) $. We consider $k$-radio labelings of $G$ when $ k = \text{diam} (G)$. In this setting, $f$ is injective; if $f$ is also surjective onto $ {1, 2, . . ., |V (G)|} $, then $f$ is a consecutive radio labeling. Graphs that can be labeled with such a labeling are called radio graceful. In this paper, we give two results on the existence of radio graceful Hamming graphs. The main result shows that the Cartesian product of $t$ copies of a complete graph is radio graceful for certain $t$. Graphs of this form provide infinitely many examples of radio graceful graphs of arbitrary diameter. We also show that these graphs are not radio graceful for large $t$.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2016, 36, 4; 1007-1020
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-11 z 11

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