Manoj Changat

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A profile on a graph G is any nonempty multiset whose elements are vertices from G. The corresponding remoteness function associates to each vertex x ∈ V (G) the sum of distances from x to the vertices in the profile. Starting from some nice and useful properties of the remoteness function in hypercubes, the remoteness function is studied in arbitrary(More)
A feasible family of paths in a connected graphG is a family that contains at least one path between any pair of vertices in G. Any feasible path family defines a convexity on G. Well-known instances are: the geodesics, the induced paths, and all paths. We propose a more general approach for such ‘path properties’. We survey a number of results from this(More)
The induced path transit function J (u; v) in a graph consists of the set of all vertices lying on any induced path between the vertices u and v. A transit function J satis2es monotone axiom if x; y∈ J (u; v) implies J (x; y) ⊆ J (u; v). A transit function J is said to satisfy the Peano axiom if, for any u; v; w∈V; x∈ J (v; w), y∈ J (u; x), there is a z ∈ J(More)
The distance DG(v) of a vertex v in an undirected graph G is the sum of the distances between v and all other vertices of G. The set of vertices in G with maximum (minimum) distance is the antimedian (median) set of a graph G. It is proved that for arbitrary graphs G and J and a positive integer r ≥ 2, there exists a connected graph H such that G is the(More)
An antimedian of a profile π = (x1, x2, . . . , xk) of vertices of a graph G is a vertex maximizing the sum of the distances to the elements of the profile. The antimedian function is defined on the set of all profiles on G and has as output the set of antimedians of a profile. It is a typical location function for finding a location for an obnoxious(More)
The geodesic and induced path transit functions are the two well-studied interval functions in graphs. Two important transit functions related to the geodesic and induced path functions are the triangle path transit functions which consist of all vertices on all u, v-shortest (induced) paths or all vertices adjacent to two adjacent vertices on all u,(More)
Interactions among the scientific community implicitly and explicitly reflects technological and scientific progress in any industry. Direct interactions can be found in the scientific publications and are evident from various affiliations in such publications. In this work, important finding about Information technology for engineering is revealed using(More)
A graph G is strongly distance-balanced if for every edge uv of G and every i ≥ 0 the number of vertices x with d(x, u) = d(x, v) − 1 = i equals the number of vertices y with d(y, v) = d(y, u) − 1 = i. It is proved that the strong product of graphs is strongly distance-balanced if and only if both factors are strongly distance-balanced. It is also proved(More)