The localization game is a pursuit-evasion analogous to Cops and Robbers, where the robber invisible cops send distance probes in an attempt identify location of robber. We present novel graph parameter called capture time, which measures how long lasts assuming optimal play. conjecture that time linear order graph, show holds for families such as trees interval graphs. study bounds on its mono...

given a non-abelian finite group $g$, let $pi(g)$ denote the set of prime divisors of the order of $g$ and denote by $z(g)$ the center of $g$. thetextit{ prime graph} of $g$ is the graph with vertex set $pi(g)$ where two distinct primes $p$ and $q$ are joined by an edge if and only if $g$ contains an element of order $pq$ and the textit{non-commuting graph} of $g$ is the graph with the vertex s...

In this research article, we apply the concept of interval-valued neutrosophic sets to graph structures. We present the concept of interval-valued neutrosophic graph structures. We describe certain operations on interval-valued neutrosophic graph structures and elaborate them with appropriate examples. Further, we investigate some relevant properties of these operators. Moreover, we propose som...

In graph-structured data, the node content contains rich information. Therefore, how to effectively utilize is crucial improve performance of graph convolutional networks (GCNs) on various analytical tasks. However, current GCNs do not fully content, especially multi-order content. For example, attention (GATs) only focus low-order while high-order completely ignored. To address this issue, we ...