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

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

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.

Fast Many-to-Many Routing for Dynamic Taxi Sharing with Meeting Points

We introduce an improved algorithm for the dynamic taxi sharing problem, i.e. a dispatcher that schedules a fleet of shared taxis as it is used by services like UberXShare and Lyft Shared. We speed up the basic online algorithm that looks for all possible insertions of a new customer into a set of existing routes, we generalize the objective function, and we efficiently support a large number of possible pick-up and drop-off locations. This lays an algorithmic foundation for taxi sharing systems with higher vehicle occupancy - enabling greatly reduced cost and ecological impact at comparable service quality. We find that our algorithm computes assignments between vehicles and riders several times faster than a previous state-of-the-art approach. Further, we observe that allowing meeting points for vehicles and riders can reduce the operating cost of vehicle fleets by up to 15% while also reducing rider wait and trip times.Comment: 26 pages, 7 figures, 4 tables. To be presented at ALENEX'24. arXiv admin note: substantial text overlap with arXiv:2305.0541

Rational coordination of crowdsourced resources for geo-temporal request satisfaction

Existing mobile devices roaming around the mobility field should be considered as useful resources in geo-temporal request satisfaction. We refer to the capability of an application to access a physical device at particular geographical locations and times as GeoPresence, and we pre- sume that mobile agents participating in GeoPresence-capable applica- tions should be rational, competitive, and willing to deviate from their routes if given the right incentive. In this paper, we define the Hitch- hiking problem, which is that of finding the optimal assignment of re- quests with specific spatio-temporal characteristics to competitive mobile agents subject to spatio-temporal constraints. We design a mechanism that takes into consideration the rationality of the agents for request sat- isfaction, with an objective to maximize the total profit of the system. We analytically prove the mechanism to be convergent with a profit com- parable to that of a 1/2-approximation greedy algorithm, and evaluate its consideration of rationality experimentally.Supported in part by NSF Grants; #1430145, #1414119, #1347522, #1239021, and #1012798

The 1/3-conjectures for domination in cubic graphs

A set S of vertices in a graph G is a dominating set of G if every vertex not in S is adjacent to a vertex in S . The domination number of G, denoted by $\gamma$(G), is the minimum cardinality of a dominating set in G. In a breakthrough paper in 2008, L{\"o}wenstein and Rautenbach proved that if G is a cubic graph of order n and girth at least 83, then $\gamma$(G) $\le$ n/3. A natural question is if this girth condition can be lowered. The question gave birth to two 1/3-conjectures for domination in cubic graphs. The first conjecture, posed by Verstraete in 2010, states that if G is a cubic graph on n vertices with girth at least 6, then $\gamma$(G) $\le$ n/3. The second conjecture, first posed as a question by Kostochka in 2009, states that if G is a cubic, bipartite graph of order n, then $\gamma$(G) $\le$n/3. In this paper, we prove Verstraete's conjecture when there is no 7-cycle and no 8-cycle, and we prove the Kostochka's related conjecture for bipartite graphs when there is no 4-cycle and no 8-cycle

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