a vertex irregular total k-labeling of a graph g with vertex set v and edge set e is an assignment of positive integer labels {1, 2, ..., k} to both vertices and edges so that the weights calculated at vertices are distinct. the total vertex irregularity strength of g, denoted by tvs(g)is the minimum value of the largest label k over all such irregular assignment. in this paper, we study the to...

A chord of a path $P$ is an edge joining two non-adjacent vertices of $P$. A path  $P$ is called a monophonic path if it is a chordless path. A longest $x-y$ monophonic path is called an $x-y$ detour monophonic path. A  detour monophonic graphoidal cover of a graph $G$ is a collection $psi_{dm}$ of detour monophonic paths in $G$ such that every vertex of $G$ is an internal vertex  of at most on...

Good importance sampling strategies are decisive for the quality and robustness of photorealistic image synthesis with Monte Carlo integration. Path guiding approaches use transport paths sampled by an existing base sampler to build refine a distribution. This distribution then guides subsequent in regions that otherwise hard sample. We observe all terms measurement contribution function during...

A 3-path vertex cover in a graph is a vertex subset C such that every path of three vertices contains at least one vertex from C. The parameterized 3-path vertex cover problem asks whether a graph has a 3-path vertex cover of size at most k. In this paper, we give a kernel of 5k vertices and an O(1.7485)-time polynomial-space algorithm for this problem, both new results improve previous known b...

For a given source vertex (node) in the graph, the algorithm finds the path with lowest cost (i.e. the shortest path) between that vertex and every other vertex. It can also be used for finding costs of shortest paths from a single vertex to a single destination vertex by stopping the algorithm once the shortest path to the destination vertex has been determined. For example, if the vertices of...

For a graph G and a positive integer k, a subset S of vertices of G is called a k-path vertex cover if every path of order k inG contains at least one vertex from S. The cardinality of a minimum k-path vertex cover is denoted by ψk(G). In this paper, we give some bounds and the exact values in special cases for ψk of the Cartesian, and lexicographic products of some graphs. Key–Words: Vertex co...