http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
ON REFORMULATED INJECTIVE CHROMATIC INDEX OF GRAPHS
SALEH, ANWAR,AQEEL, A.,ALASHWALI, HANAA The Korean Society for Computational and Applied M 2021 Journal of applied mathematics & informatics Vol.39 No.1
For a graph G = (V, E), a vertex coloring (or, simply, a coloring) of G is a function C : V (G) → {1, 2, …, k} (using the non-negative integers {1, 2, …, k} as colors). We say that a coloring of a graph G is injective if for every vertex v ∈ V (G), all the neighbors of v are assigned with distinct colors. The injective chromatic number χi(G) of a graph G is the least k such that there is an injective k-coloring [6]. In this paper, we study a natural variation of the injective coloring problem: coloring the edges of a graph under the same constraints (alternatively, to investigate the injective chromatic number of line graphs), we define the k- injective edge coloring of a graph G as a mapping C : E(G) → {1, 2, …, k}, such that for every edge e ∈ E(G), all the neighbors edges of e are assigned with distinct colors. The injective chromatic index χ′in(G) of G is the least positive integer k such that G has k- injective edge coloring, exact values of the injective chromatic index of different families of graphs are obtained, some related results and bounds are established. Finally, we define the injective clique number ωin and state a conjecture, that, for any graph G, ωin ≤ χ′in(G) ≤ ωin + 2.
UPHILL ZAGREB INDICES OF SOME GRAPH OPERATIONS FOR CERTAIN GRAPHS
SALEH, ANWAR,BAZHEAR, SARA,MUTHANA, NAJAT The Korean Society for Computational and Applied M 2022 Journal of applied mathematics & informatics Vol.40 No.5-6
The topological indices are numerical parameters which determined the biological, physical and chemical properties based on the structure of the chemical compounds. One of the recently topological indices is the uphill Zagreb indices. In this paper, the formulae of some uphill Zagreb indices for a few graph operations of some graphs have been derived. Furthermore, the precise formulae of those indices for the honeycomb network have been found along with their graphical profiles.
Distance Eccentric Connectivity Index of Graphs
Akram Alqesmah,Anwar Saleh,R. Rangarajan,Aysun Yurttas Gunes,Ismail Naci CANGUL 경북대학교 자연과학대학 수학과 2021 Kyungpook mathematical journal Vol.61 No.1
Let G = (V, E) be a connected graph. The eccentric connectivity index of G is defined by ξC (G) = ∑u∈V (G) deg(u)e(u), where deg(u) and e(u) denote the degree and eccentricity of the vertex u in G, respectively. In this paper, we introduce a new formulation of ξC that will be called the distance eccentric connectivity index of G and defined by ξDe(G) = ∑u∈V (G) degDe(u)e(u) where degDe(u) denotes the distance eccentricity degree of the vertex u in G. The aim of this paper is to introduce and study this new topological index. The values of the eccentric connectivity index is calculated for some fundamental graph classes and also for some graph operations. Some inequalities giving upper and lower bounds for this index are obtained.