The Preservation and Authenticity of Ḥadīth As a Source of Sīrah: A Critique of Robert Spencer’S Views on Historicity of Muḥammad

The account of the deeds and sayings of the prophet (ﷺ) has been carefully preserved since the dawn of Islam. This is what actually led Ernest Renan to believe that “[Islam] was born in the full light of history”, and that the life of Muḥammad (ﷺ) can be known as explicitly as that of any sixteenth century reformer. Notwithstanding, some contemporary writers doubt the historicity of Muḥammad (ﷺ) ; Robert Spencer is one of them. He is an American author. He is quite famous for his criticism of Islam and the prophet of Islam. He has published twelve books so far. He is a member of Melkite Greek Catholic Church. He contends that Muḥammad’s (ﷺ) historical value is in no way greater and more reliable than mythological figures or characters such as Robin Hood and Macbeth. He maintains that the very idea of subjecting the traditionally accepted account of the life of Muḥammad (ﷺ) and the origins of Islam will be regarded by many Muslims as an affront. To substantiate his argument, he rigorously criticizes the historical value of ḥadīth. He argues that aḥādīth were fabricated and compiled in the third century. He maintains that aḥādīth were concocted much later to be used as weapons in political strife and religious controversies. This paper is an academic attempt to prove that aḥādīth were painstakingly preserved and for that purpose various techniques were employed. Besides, it also sheds light on the reasons for the fabrication of aḥādīth and the ways and means utilized for sifting the genuine aḥādīth from forgeries. Findings of this article suggest that the minute details of the life of Muḥammad (ﷺ) have been scrupulously preserved; hence aḥādīth can be used as a reliable source of Sīrah.

Some Vertex-Degree-Based Topological Indices of Graphs

Many topological indices which are being used by researchers in the quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies to predict the physico-chemical properties of molecules, are based on vertex degrees of the corresponding molecular graphs. When a new topological index is introduced in chemical graph theory, one of the important questions that need to be answered is for which members of a certain class of n-vertex graphs this index assumes minimal and maximal values? On the other hand, there are many well known graph families and vertex-degree-based topological indices in the literature for which this question remains open. The main purpose of current study is to address this open question for some well known families of graphs. Firstly, the collection of all k-polygonal chains (for k = 3, 4, 5) with fixed number of k-polygons is considered and the extremal elements from this family are characterized with respect to several well known bond incident degree (BID) indices (BID indices form a subclass of the class of all vertex-degree-based topological indices). From the derived results, many already reported results are obtained as corollaries. Furthermore, the extremal 4-polygonal (polyomino) chains for some renowned vertex-degree-based topological indices (other than BID indices) are also determined. Next, the problem of characterizing the extremal cacti over the certain classes of cacti (tree-like polyphenylene systems, spiro hexagonal systems and general cacti) with some fixed parameters is addressed for various well known vertex-degree-based topological indices. Finally, some mathematical properties of the atom-bond connectivity index and augmented Zagreb index are explored