The Detour Domination and Connected Detour Domination values of a graph

The number of -sets that  belongs to in G is defined as the detour domination value of indicated by for each vertex . In this article, we examined at the concept of a graph’s detour domination value. The connected detour domination values of a vertex  represented as  , are defined as the number of -sets to which a vertex belongs  to G. Some of the related detour dominating values in graphs’ general characteristics are examined. This concept’s satisfaction of some general properties is investigated. Some common graphs are established

Detour Global Domination for Degree Splitting graphs of some graphs

In this paper, we introduced the new concept detour global domination number for degree splitting graph of standard graphs. The detour global dominating sets in some standard and special graphs are determined. First we recollect the concept of degree splitting graph of a graph and we produce some results based on the detour global domination number of degree splitting graph of star graph, bistar graph, complete bipartite graph, complete graph path graph, cycle graph, wheel graph and helm graph. A set S is called a detour global dominating set of G if S is both detour and global dominating set of G. The detour global domination number is the minimum cardinality of a detour global dominating set in G

Multiple domination models for placement of electric vehicle charging stations in road networks

Electric and hybrid vehicles play an increasing role in the road transport networks. Despite their advantages, they have a relatively limited cruising range in comparison to traditional diesel/petrol vehicles, and require significant battery charging time. We propose to model the facility location problem of the placement of charging stations in road networks as a multiple domination problem on reachability graphs. This model takes into consideration natural assumptions such as a threshold for remaining battery load, and provides some minimal choice for a travel direction to recharge the battery. Experimental evaluation and simulations for the proposed facility location model are presented in the case of real road networks corresponding to the cities of Boston and Dublin.Comment: 20 pages, 5 figures; Original version from March-April 201

Outer independent square free detour number of a graph

For a connected graph , a set  of vertices is called an outer independent square free detour set if   is a square free detour set of  such that either  or is an independent set. The minimum cardinality of an outer independent square free detour set of  is called an outer independent square free detour number of  and is denoted by  We determine the outer independent square free detour number of some graphs. We characterize the graph which realizes the result that for any pair of integers  and  with there exists a connected graph  of order  with square free detour number and outer independent square free detour number

Detour Polynomials of Generalized Vertex Identified of Graphs

تعد مسافة الالتفاف من أهم أنواع المسافات التي لها تطبيقات حديثة في الكيمياء وشبكات الكمبيوتر، لذلك حصلنا في هذا البحث على متعددات حدود الالتفاف وأدلتها لـ  nمن البيانات المنفصلة عن بعضها البعض بالنسبة للرؤوس ، n≥3. أيضًا وجدنا متعددات حدود الالتفاف وأدلتها لبعض البيانات الخاصة والتي لها تطبيقات مهمة في الكيمياء.The Detour distance is one of the most common distance types used in chemistry and computer networks today. Therefore, in this paper, the detour polynomials and detour indices of vertices identified of n-graphs which are connected to themselves and separated from each other with respect to the vertices for n≥3 will be obtained. Also, polynomials detour and detour indices will be found for another graphs which have important applications in Chemistry.

The hub number of a fuzzy graph

In this paper, we introduced the concepts of hub number in fuzzy graph and is denoted by h(G). The hub number of fuzzy graph G is the minimum fuzzy cardinality among all minimal fuzzy hub sets . We determine the hub number h(G) for several classes of fuzzy graph and obtain Nordhaus-Gaddum type results for this parameter. Further, some bounds of h(G) are investigated. Also the relations between h(G) and other known parameters in fuzzy graphs are investigated.Publisher's Versio

On paths and cycles dominating hypercubes

AbstractThe aim of the present paper is to study the properties of the hypercube related to the concept of domination. We derive upper and lower bounds and prove an interpolation theorem for related invariants

The Outer Connected Detour Monophonic Number of a Graph

For a connected graph ???? = (????, ????) of order  a set is called a monophonic set of ????if every vertex of ????is contained in a monophonic path joining some pair of vertices in ????. The monophonic number (????) of is the minimum cardinality of its monophonic sets. If  or the subgraph  is connected, then a detour monophonic set  of a connected graph is said to be an outer connected detour monophonic setof .The outer connecteddetourmonophonic number of , indicated by the symbol , is the minimum cardinality of an outer connected detour monophonic set of . The outer connected detour monophonic number of some standard graphs are determined. It is shown that for positive integers , and ???? ≥ 2 with ,there exists a connected graph ????with???????????????????? = , ????????????m???????? = and  = ????. Also, it is shown that for every pair of integers ????and b with 2 ≤ ???? ≤ ????, there exists a connected graph with and